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Octahedral Number -- from Wolfram MathWorld

A figurate number which is the sum of two consecutive pyramidal numbers, O_n=P_(n-1)+P_n=1/3n(2n^2+1). (1) The first few are 1, 6, 19, 44, 85, 146, 231, 344, 489, 670, 891, 1156, ... (OEIS A005900). The generating function for the octahedral numbers is (x(x+1)^2)/((x-1)^4)=x+6x^2+19x^3+44x^4+.... (2) Pollock (1850) conjectured that every number is the sum of at most 7 octahedral numbers (Dickson 2005, p. 23). A related set of numbers is the number of cubes in the Haűy...



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Octahedral Number -- from Wolfram MathWorld

https://mathworld.wolfram.com/OctahedralNumber.html

A figurate number which is the sum of two consecutive pyramidal numbers, O_n=P_(n-1)+P_n=1/3n(2n^2+1). (1) The first few are 1, 6, 19, 44, 85, 146, 231, 344, 489, 670, 891, 1156, ... (OEIS A005900). The generating function for the octahedral numbers is (x(x+1)^2)/((x-1)^4)=x+6x^2+19x^3+44x^4+.... (2) Pollock (1850) conjectured that every number is the sum of at most 7 octahedral numbers (Dickson 2005, p. 23). A related set of numbers is the number of cubes in the Haűy...



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https://mathworld.wolfram.com/OctahedralNumber.html

Octahedral Number -- from Wolfram MathWorld

A figurate number which is the sum of two consecutive pyramidal numbers, O_n=P_(n-1)+P_n=1/3n(2n^2+1). (1) The first few are 1, 6, 19, 44, 85, 146, 231, 344, 489, 670, 891, 1156, ... (OEIS A005900). The generating function for the octahedral numbers is (x(x+1)^2)/((x-1)^4)=x+6x^2+19x^3+44x^4+.... (2) Pollock (1850) conjectured that every number is the sum of at most 7 octahedral numbers (Dickson 2005, p. 23). A related set of numbers is the number of cubes in the Haűy...

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      Octahedral Number -- from Wolfram MathWorld
    • DC.Title
      Octahedral Number
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      A figurate number which is the sum of two consecutive pyramidal numbers, O_n=P_(n-1)+P_n=1/3n(2n^2+1). (1) The first few are 1, 6, 19, 44, 85, 146, 231, 344, 489, 670, 891, 1156, ... (OEIS A005900). The generating function for the octahedral numbers is (x(x+1)^2)/((x-1)^4)=x+6x^2+19x^3+44x^4+.... (2) Pollock (1850) conjectured that every number is the sum of at most 7 octahedral numbers (Dickson 2005, p. 23). A related set of numbers is the number of cubes in the Haűy...
    • description
      A figurate number which is the sum of two consecutive pyramidal numbers, O_n=P_(n-1)+P_n=1/3n(2n^2+1). (1) The first few are 1, 6, 19, 44, 85, 146, 231, 344, 489, 670, 891, 1156, ... (OEIS A005900). The generating function for the octahedral numbers is (x(x+1)^2)/((x-1)^4)=x+6x^2+19x^3+44x^4+.... (2) Pollock (1850) conjectured that every number is the sum of at most 7 octahedral numbers (Dickson 2005, p. 23). A related set of numbers is the number of cubes in the Haűy...

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      Octahedral Number -- from Wolfram MathWorld
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      A figurate number which is the sum of two consecutive pyramidal numbers, O_n=P_(n-1)+P_n=1/3n(2n^2+1). (1) The first few are 1, 6, 19, 44, 85, 146, 231, 344, 489, 670, 891, 1156, ... (OEIS A005900). The generating function for the octahedral numbers is (x(x+1)^2)/((x-1)^4)=x+6x^2+19x^3+44x^4+.... (2) Pollock (1850) conjectured that every number is the sum of at most 7 octahedral numbers (Dickson 2005, p. 23). A related set of numbers is the number of cubes in the Haűy...

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      Octahedral Number -- from Wolfram MathWorld
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      A figurate number which is the sum of two consecutive pyramidal numbers, O_n=P_(n-1)+P_n=1/3n(2n^2+1). (1) The first few are 1, 6, 19, 44, 85, 146, 231, 344, 489, 670, 891, 1156, ... (OEIS A005900). The generating function for the octahedral numbers is (x(x+1)^2)/((x-1)^4)=x+6x^2+19x^3+44x^4+.... (2) Pollock (1850) conjectured that every number is the sum of at most 7 octahedral numbers (Dickson 2005, p. 23). A related set of numbers is the number of cubes in the Haűy...
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