A100214 a(n) = 4*n^3 + 4.

4, 8, 36, 112, 260, 504, 868, 1376, 2052, 2920, 4004, 5328, 6916, 8792, 10980, 13504, 16388, 19656, 23332, 27440, 32004, 37048, 42596, 48672, 55300, 62504, 70308, 78736, 87812, 97560, 108004, 119168, 131076, 143752, 157220, 171504, 186628, 202616, 219492

Offset: 0

Author

N. J. A. Sloane, Jan 12 2005

Keywords

• nonn
• easy

References

• T. A. Gulliver, Sequences from Cubes of Integers, Int. Math. Journal, 4 (2003), 439-445.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A001093.

Programs

Magma

[4*n^3+4: n in [0..40]]; // Vincenzo Librandi, Jun 15 2011

Mathematica

4*(Range[0,50]^3 +1) (* G. C. Greubel, Mar 29 2024 *)

SageMath

[4*(n^3+1) for n in range(41)] # G. C. Greubel, Mar 29 2024

Formula

From R. J. Mathar, Feb 26 2008: (Start)

O.g.f.: 28/(1-x)^2 - 48/(1-x)^3 + 24/(1-x)^4.

a(n) = 4*A001093(n). (End)

E.g.f.: 4*(1 + x + 3*x^2 + x^3)*exp(x). - G. C. Greubel, Mar 29 2024