A017463 a(n) = (11*n + 6)^3.

216, 4913, 21952, 59319, 125000, 226981, 373248, 571787, 830584, 1157625, 1560896, 2048383, 2628072, 3307949, 4096000, 5000211, 6028568, 7189057, 8489664, 9938375, 11543176, 13312053, 15252992, 17373979, 19683000, 22188041, 24897088, 27818127, 30959144

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Powers of the form (11*n+6)^m: A017461 (m=1), A017462 (m=2), this sequence (m=3), A017464 (m=4), A017465 (m=5), A017466 (m=6), A017467 (m=7), A017468 (m=8), A017469 (m=9), A017470 (m=10), A017471 (m=11), A017472 (m=12).

Programs

GAP

List([0..40], n-> (11*n+6)^3); # G. C. Greubel, Sep 19 2019

Magma

[(11*n+6)^3: n in [0..40]]; // Vincenzo Librandi, Sep 03 2011

Maple

seq((11*n+6)^3, n=0..40); # G. C. Greubel, Sep 19 2019

Mathematica

(* From Harvey P. Dale, May 16 2012 : (Start) *)
(11Range[0,40]+6)^3
LinearRecurrence[{4,-6,4,-1}, {216,4913, 21952,59319}, 40] (* End *)

PARI

vector(40, n, (11*n-5)^3) \\ G. C. Greubel, Sep 19 2019

Sage

[(11*n+6)^3 for n in (0..40)] # G. C. Greubel, Sep 19 2019

Formula

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=216, a(1)=4913, a(2)=21952, a(3)=59319. - Harvey P. Dale, May 16 2012

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

G.f.: (216 +4049*x +3596*x^2 +125*x^3)/(1-x)^4.

E.g.f.: (216 +4697*x +6171*x^2 +1331*x^3)*exp(x). (End)