A017513 a(n) = (11*n + 10)^5.

100000, 4084101, 33554432, 147008443, 459165024, 1160290625, 2535525376, 4984209207, 9039207968, 15386239549, 24883200000, 38579489651, 57735339232, 83841135993, 118636749824, 164130859375, 222620278176, 296709280757, 389328928768, 503756397099

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Powers of the form (11*n+10)^m: A017509 (m=1), A017510 (m=2), A017511 (m=3), A017512 (m=4), this sequence (m=5), A017514 (m=6), A017515 (m=7), A017516 (m=8), A017517 (m=9), A017518 (m=10), A017519 (m=11), A017520 (m=12).

Programs

GAP

List([0..30], n-> (11*n+10)^5); # G. C. Greubel, Oct 29 2019

Magma

[(11*n+10)^5: n in [0..30]]; // Vincenzo Librandi, Jun 01 2016

Maple

seq((11*n+10)^5, n=0..30); # G. C. Greubel, Oct 29 2019

Mathematica

(11*Range[30] -1)^5 (* G. C. Greubel, Jun 01 2016 *)

PARI

vector(31, n, (11*n-1)^5) \\ G. C. Greubel, Oct 29 2019

Sage

[(11*n+10)^5 for n in (0..30)] # G. C. Greubel, Oct 29 2019

Formula

From Chai Wah Wu, May 31 2016: (Start)

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n > 5.

G.f.: (x^5 + 248826*x^4 + 4943366*x^3 + 10549826*x^2 + 3484101*x + 100000)/(x - 1)^6. (End)

E.g.f.: (100000 + 3984101*x + 12743115*x^2 + 9749575*x^3 + 2342560*x^4 + 161051*x^5)*exp(x). - G. C. Greubel, Jun 01 2016