A393719 Sum of next n octahedral numbers (A005900).

1, 25, 275, 1734, 7605, 26011, 74375, 185900, 418569, 867085, 1678171, 3069650, 5353725, 8964879, 14492815, 22720856, 34670225, 51650625, 75317539, 107736670, 151455941, 209585475, 285885975, 384865924, 511888025, 673285301, 876487275, 1130156650, 1444336909, 1830611255

Offset

1,2

Links

Kelvin Voskuijl, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

a(n) = (n*(n^2+1)^2*(n^2 + 2))/12.

G.f.: x*(1+17*x+103*x^2+178*x^3+103*x^4+17*x^5+x^6)/(1-x)^8.

E.g.f.: exp(x)*x*(12+138*x+406*x^2+390*x^3+144*x^4+21*x^5+x^6)/12.

Example

The octahedral numbers and their groups summed begin
  1, 6, 19, 44, 85, 146, 231, 344, 489, 670
  \/ \---/  \--------/  \---------------/
  1,   25,     275,            1734

Mathematica

A393719[n_] := (n*(n^2 + 1)^2*(n^2 + 2))/12; Array[A393719, 35] (* Paolo Xausa, Apr 15 2026 *)

Prog

(PARI) a(n) = (n*(n^2+1)^2*(n^2 + 2))/12

Crossrefs

Cf. A005900, A006325.

Cf. A260513, A072474, A372583, A075664.

Sequence in context: A329537 A012859 A010830 * A022717 A197279 A061617

Adjacent sequences: A393716 A393717 A393718 * A393720 A393721 A393722

Keyword

nonn,easy

Author

Kelvin Voskuijl, Apr 09 2026

Status

approved