A017466 a(n) = (11*n + 6)^6.

46656, 24137569, 481890304, 3518743761, 15625000000, 51520374361, 139314069504, 326940373369, 689869781056, 1340095640625, 2436396322816, 4195872914689, 6906762437184, 10942526586601, 16777216000000, 25002110044521, 36343632130624, 51682540549249, 72074394832896

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

a(0) = 46656, a(1) = 24137569, a(2) = 481890304, a(3) = 3518743761, a(4) = 15625000000, a(5) = 51520374361, a(6) = 139314069504, 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). - Harvey P. Dale, Jan 19 2013

From G. C. Greubel, Sep 19 2019: (Start)

G.f.: (46656 +23810977*x +313907097*x^2 +650767622*x^3 +270308102*x^4 +16667841*x^5 +15625*x^6)/(1-x)^7.

E.g.f.: (46656 +24090913*x +216830911*x^2 +357573150*x^3 +181035965*x^4 +32371251*x^5 +1771561*x^6)*exp(x). (End)

Maple

seq((11*n+6)^6, n=0..20); # G. C. Greubel, Sep 19 2019

Mathematica

(11 * Range[0, 20] + 6)^6 (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {46656, 24137569, 481890304, 3518743761, 15625000000, 51520374361, 139314069504}, 20] (* Harvey P. Dale, Jan 19 2013 *)

Prog

(Magma) [(11*n+6)^6: n in [0..20]]; // Vincenzo Librandi, Sep 04 2011
(PARI) a(n)=(11*n+6)^6 \\ Charles R Greathouse IV, Nov 04 2017
(Sage) [(11*n+6)^6 for n in (0..20)] # G. C. Greubel, Sep 19 2019
(GAP) List([0..20], n-> (11*n+6)^6); # G. C. Greubel, Sep 19 2019

Crossrefs

Powers of the form (11*n+6)^m: A017461 (m=1), A017462 (m=2), A017463 (m=3), A017464 (m=4), A017465 (m=5), this sequence (m=6), A017467 (m=7), A017468 (m=8), A017469 (m=9), A017470 (m=10), A017471 (m=11), A017472 (m=12).

Sequence in context: A017238 A223275 A017346 * A017598 A223362 A143163

Adjacent sequences: A017463 A017464 A017465 * A017467 A017468 A017469

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved