A017504 a(n) = (11*n + 9)^8.

43046721, 25600000000, 852891037441, 9682651996416, 62259690411361, 281474976710656, 1001129150390625, 2992179271065856, 7837433594376961, 18509302102818816, 40213853471634241, 81573072100000000

Offset

0,1

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).

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, Dec 25 2013

From G. C. Greubel, Oct 28 2019: (Start)

G.f.: (43046721 +25212579511*x +624040719397*x^2 +2924616734883*x^3 + 3674923678339*x^4 +1290563847493*x^5 +102733746903*x^6 +815728417*x^7 + 256*x^8)/(1-x)^9.

E.g.f.: (43046721 +25556953279*x +400867042081*x^2 +1200122639562*x^3 +

1189336320711*x^4 +488350759974*x^5 +90501965246*x^6 +7405124980*x^7 + 214358881*x^8)*exp(x). (End)

Maple

seq((11*n+9)^8, n=0..20); # G. C. Greubel, Oct 28 2019

Mathematica

(11*Range[0, 20]+9)^8 (* or *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {43046721, 25600000000, 852891037441, 9682651996416, 62259690411361, 281474976710656, 1001129150390625, 2992179271065856, 7837433594376961}, 20] (* Harvey P. Dale, Dec 25 2013 *)

Prog

(PARI) vector(21, n, (11*n-2)^8) \\ G. C. Greubel, Oct 28 2019
(Magma) [(11*n+9)^8: n in [0..20]]; // G. C. Greubel, Oct 28 2019
(Sage) [(11*n+9)^8 for n in (0..20)] # G. C. Greubel, Oct 28 2019
(GAP) List([0..20], n-> (11*n+9)^8); # G. C. Greubel, Oct 28 2019

Crossrefs

Powers of the form (11*n+9)^m: A017497 (m=1), A017498 (m=2), A017499 (m=3), A017500 (m=4), A017501 (m=5), A017502 (m=6), A017503 (m=7), this sequence (m=8), A017505 (m=9), A017506 (m=10), A017607 (m=11), A017508 (m=12).

Subsequence of A001016.

Sequence in context: A017084 A017168 A017384 * A017636 A139029 A206326

Adjacent sequences: A017501 A017502 A017503 * A017505 A017506 A017507

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved