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

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

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+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.

Programs

GAP

List([0..20], n-> (11*n+9)^8); # G. C. Greubel, Oct 28 2019

Magma

[(11*n+9)^8: n in [0..20]]; // G. C. Greubel, Oct 28 2019

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 *)

PARI

vector(21, n, (11*n-2)^8) \\ G. C. Greubel, Oct 28 2019

Sage

[(11*n+9)^8 for n in (0..20)] # G. C. Greubel, Oct 28 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, Dec 25 2013

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

G.f.: (43046721 [phone]*x [phone]*x^2 [phone]*x^3 + 3674923678339*x^4 [phone]*x^5 [phone]*x^6 [phone]*x^7 + 256*x^8)/(1-x)^9.

E.g.f.: (43046721 [phone]*x [phone]*x^2 [phone]*x^3 +

1189336320711*x^4 [phone]*x^5 [phone]*x^6 [phone]*x^7 + 214358881*x^8)*exp(x). (End)