A017501 a(n) = (11*n + 9)^5.

59049, 3200000, 28629151, 130691232, 418195493, 1073741824, 2373046875, 4704270176, 8587340257, 14693280768, 23863536599, 37129300000, 55730836701, 81136812032, 115063617043, 159494694624

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+9)^m: A017497 (m=1), A017498 (m=2), A017499 (m=3), A017500 (m=4), this sequence (m=5), A017502 (m=6), A017503 (m=7), A017504 (m=8), A017505 (m=9), A017506 (m=10), A017607 (m=11), A017508 (m=12).

Subsequence of A000584.

Programs

GAP

List([0..20], n-> (11*n+9)^5); # G. C. Greubel, Oct 28 2019

Magma

[(11*n+9)^5: n in [0..20]]; // G. C. Greubel, Oct 28 2019

Maple

seq((11*n+9)^5, n=0..20); # G. C. Greubel, Oct 28 2019

Mathematica

(11*Range[0,20]+9)^5 (* or *) LinearRecurrence[{6,-15,20,-15,6,-1}, {59049,3200000,28629151,130691232,418195493,1073741824},20] (* Harvey P. Dale, Jan 25 2013 *)

PARI

vector(21, n, (11*n-2)^5) \\ G. C. Greubel, Oct 28 2019

Sage

[(11*n+9)^5 for n in (0..20)] # G. C. Greubel, Oct 28 2019

Formula

a(0)=59049, a(1)=3200000, a(2)=28629151, a(3)=130691232, a(4)=418195493, a(5)=1073741824, 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). - Harvey P. Dale, Jan 25 2013

G.f.: (59049 + 2845706*x + 10314886*x^2 + 5735346*x^3 + 371101*x^4 + 32*x^5) / (1-x)^6. - Harvey P. Dale, Jan 25 2013

E.g.f.: (59049 + 3140951*x + 11144100*x^2 + 9057455*x^3 + 2269355*x^4 + 161051*x^5)*exp(x). - G. C. Greubel, Oct 28 2019