A017514 a(n) = (11*n + 10)^6.

1000000, 85766121, 1073741824, 6321363049, 24794911296, 75418890625, 192699928576, 433626201009, 885842380864, 1677100110841, 2985984000000, 5053913144281, 8198418170944, 12827693806929, 19456426971136

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+10)^m: A017509 (m=1), A017510 (m=2), A017511 (m=3), A017512 (m=4), A017513 (m=5), this sequence (m=6), A017515 (m=7), A017516 (m=8), A017517 (m=9), A017518 (m=10), A017519 (m=11), A017520 (m=12).

Programs

GAP

List([0..20], n-> (11*n+10)^6); # G. C. Greubel, Oct 29 2019

Magma

[(11*n+10)^6: n in [0..20]]; // G. C. Greubel, Oct 29 2019

Maple

seq((11*n+10)^6, n=0..20); # G. C. Greubel, Oct 29 2019

Mathematica

(11*Range[0,20]+10)^6 (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1}, {1000000, 85766121,1073741824,6321363049,24794911296, 75418890625, 192699928576},20] (* Harvey P. Dale, Apr 21 2012 *)

Maxima

makelist((11*n+10)^6,n,0,30); /* Martin Ettl, Oct 21 2012 */

PARI

vector(21, n, (11*n-1)^6) \\ G. C. Greubel, Oct 29 2019

Sage

[(11*n+10)^6 for n in (0..20)] # G. C. Greubel, Oct 29 2019

Formula

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7); a(0)=1000000, a(1)=85766121, a(2)=1073741824, a(3)=6321363049, a(4)=24794911296, a(5)=75418890625, a(6)=192699928576. - Harvey P. Dale, Apr 21 2012

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

G.f.: (1000000 + 78766121*x + 494378977*x^2 + 571258822*x^3 + 127134022*x^4 + 2985977*x^5 + x^6)/(1-x)^7.

E.g.f.: (1000000 + 84766121*x + 451604791*x^2 + 559405990*x^3 + 233743565*x^4 + 36236475*x^5 + 1771561*x^6)*exp(x). (End)