A017224 a(n) = (9*n + 5)^4.

625, 38416, 279841, 1048576, 2825761, 6250000, 12117361, 21381376, 35153041, 54700816, 81450625, 116985856, 163047361, 221533456, 294499921, 384160000, 492884401, 623201296, 777796321, 959512576

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 (5,-10,10,-5,1).

Crossrefs

Sequences of the form (9*n+5)^k: A017221 (k=1), A017222 (k=2), A017223 (k=3), this sequence (k=4), A017225 (k=5), A017226 (k=6), A017227 (k=7), A017228 (k=8), A017229 (k=9), A017230 (k=10), A017231 (k=11).

Cf. A000583 (n^4).

Programs

Magma

[(9*n+5)^4: n in [0..35]] ; // Vincenzo Librandi, Jul 24 2011

Mathematica

(9*Range[0,20]+5)^4 (* Harvey P. Dale, Apr 27 2016 *)

SageMath

[(9*n+5)^4 for n in range(41)] # G. C. Greubel, Jan 06 2023

Formula

a(n) = A000583(A017221(n)).

From Harvey P. Dale, Apr 27 2016: (Start)

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

G.f.: (625 + 35291*x + 94011*x^2 + 27281*x^3 + 256*x^4)/(1-x)^5. (End)

E.g.f.: (625 + 37791*x + 101817*x^2 + 53946*x^3 + 6561*x^4)*exp(x). - G. C. Greubel, Jan 06 2023