A017502 a(n) = (11*n + 9)^6.

531441, 64000000, 887503681, 5489031744, 22164361129, 68719476736, 177978515625, 404567235136, 832972004929, 1586874322944, 2839760855281, 4826809000000, 7858047974841, 12332795428864, 18755369578009

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 (7,-21,35,-35,21,-7,1).

Crossrefs

Powers of the form (11*n+9)^m: A017497 (m=1), A017498 (m=2), A017499 (m=3), A017500 (m=4), A017501 (m=5), this sequence (m=6), A017503 (m=7), A017504 (m=8), A017505 (m=9), A017506 (m=10), A017607 (m=11), A017508 (m=12).

Subsequence of A001014.

Programs

GAP

List([0..20], n-> (11*n+9)^6); # G. C. Greubel, Oct 28 2019

Magma

[(11*n+9)^6: n in [0..20]]; // G. C. Greubel, Oct 28 2019

Maple

seq((11*n+9)^6, n=0..20); # G. C. Greubel, Oct 28 2019

Mathematica

(11Range[0,20]+9)^6 (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1}, {531441,64000000,887503681,5489031744,22164361129,68719476736, 177978515625}, 20] (* Harvey P. Dale, Dec 06 2018 *)

Maxima

makelist((11*n+9)^6, n, 0, 30); /* Martin Ettl, Oct 21 2012 */

PARI

vector(21, n, (11*n-2)^6) \\ G. C. Greubel, Oct 28 2019

Sage

[(11*n+9)^6 for n in (0..20)] # G. C. Greubel, Oct 28 2019

Formula

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

G.f.: (531441 + 60279913*x + 450663942*x^2 + 601905542*x^3 + 157316657*x^4 + 4826361*x^5 + 64*x^6)/(1-x)^7.

E.g.f.: (531441 + 63468559*x + 380017561*x^2 + 502998210*x^3 + 219907820*x^4 + 35270169*x^5 + 1771561*x^6)*exp(x). (End)