A017516 a(n) = (11*n + 10)^8.

100000000, 37822859361, 1099511627776, 11688200277601, 72301961339136, 318644812890625, 1113034787454976, 3282116715437121, 8507630225817856, 19925626416901921, 42998169600000000, 86730203469006241

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 (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Powers of the form (11*n+10)^m: A017509 (m=1), A017510 (m=2), A017511 (m=3), A017512 (m=4), A017513 (m=5), A017514 (m=6), A017515 (m=7), this sequence (m=8), A017517 (m=9), A017518 (m=10), A017519 (m=11), A017520 (m=12).

Programs

GAP

List([0..20], n-> (11*n+10)^8); # G. C. Greubel, Oct 29 2019

Magma

[(11*n+10)^8: n in [0..20]]; // G. C. Greubel, Oct 29 2019

Maple

seq((11*n+10)^8, n=0..20); # G. C. Greubel, Oct 29 2019

Mathematica

(11*Range[0,20]+10)^8 (* or *) LinearRecurrence[{9,-36,84,-126,126,-84, 36,-9,1}, {100000000,37822859361,1099511627776,11688200277601, 72301961339136, 318644812890625,1113034787454976,3282116715437121, 8507630225817856}, 20] (* Harvey P. Dale, Mar 28 2015 *)

PARI

vector(21, n, (11*n-1)^8) \\ G. C. Greubel, Oct 29 2019

Sage

[(11*n+10)^8 for n in (0..20)] # G. C. Greubel, Oct 29 2019

Formula

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9). - Harvey P. Dale, Mar 28 2015

From G. C. Greubel, Oct 29 2019: (Start)

G.f.: (100000000 + 36922859361*x + 762705893527*x^2 + 3145818564613*x^3 + 3526057254339*x^4 + 1096474378339*x^5 + 74441150053*x^6 + 429981687*x^7 + x^8)/(1-x)^9.

E.g.f.: (100000000 + 37722859361*x + 511982954527*x^2 + 1417172328726*x^3 + 1333126606581*x^4 + 526757558250*x^5 + 94718280426*x^6 + 7561022348*x^7 + 214358881*x^8)*exp(x). (End)