A017223 a(n) = (9*n+5)^3.

125, 2744, 12167, 32768, 68921, 125000, 205379, 314432, 456533, 636056, 857375, 1124864, 1442897, 1815848, 2248091, 2744000, 3307949, 3944312, 4657463, 5451776, 6331625, 7301384, 8365427

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Sequences of the form (9*n+5)^k: A017221 (k=1), A017222 (k=2), this sequence (k=3), A017224 (k=4), A017225 (k=5), A017226 (k=6), A017227 (k=7), A017228 (k=8), A017229 (k=9), A017230 (k=10), A017231 (k=11).

Programs

Magma

[(9*n+5)^3: n in [0..35]] ; // Vincenzo Librandi, Jul 24 2011

Mathematica

(9*Range[0,50] + 5)^3 (* G. C. Greubel, Jan 06 2023 *)

SageMath

[(9*n+5)^3 for n in range(51)] # G. C. Greubel, Jan 06 2023

Formula

From Chai Wah Wu, Jul 14 2016: (Start)

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 3.

G.f.: (125 + 2244*x + 1941*x^2 + 64*x^3)/(1 - x)^4. (End)

E.g.f.: (125 + 2619*x + 3402*x^2 + 729*x^3)*exp(x). - G. C. Greubel, Jan 06 2023