A017450 a(n) = (11*n + 5)^2.

25, 256, 729, 1444, 2401, 3600, 5041, 6724, 8649, 10816, 13225, 15876, 18769, 21904, 25281, 28900, 32761, 36864, 41209, 45796, 50625, 55696, 61009, 66564, 72361, 78400, 84681, 91204, 97969, 104976, 112225, 119716, 127449, 135424, 143641, 152100, 160801, 169744, 178929, 188356, 198025

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 (3,-3,1).

Crossrefs

Powers of the form (11*n+5)^m: A017449 (m=1), this sequence (m=2), A017451 (m=3), A017452 (m=4), A017453 (m=5), A017454 (m=6), A017455 (m=7), A017456 (m=8), A017457 (m=9), A017458 (m=10), A017459 (m=11), A017460 (m=12).

Programs

GAP

List([0..45], n-> (11*n+5)^2); # G. C. Greubel, Sep 18 2019

Magma

[(11*n+5)^2: n in [0..45]]; // Vincenzo Librandi, Sep 03 2011

Maple

seq((11*n+5)^2, n=0..45); # G. C. Greubel, Sep 18 2019

Mathematica

(11Range[0,45]+5)^2 (* or *) LinearRecurrence[{3,-3,1},{25,256,729},45] (* Harvey P. Dale, Dec 08 2013 *)

PARI

a(n)=(11*n+5)^2 \\ Charles R Greathouse IV, Jun 17 2017

Sage

[(11*n+5)^2 for n in (0..45)] # G. C. Greubel, Sep 18 2019

Formula

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=25, a(1)=256, a(2)=729. - Harvey P. Dale, Dec 08 2013

From G. C. Greubel, Sep 18 2019: (Start)

G.f.: (25 +181*x +36*x^2)/(1-x)^3.

E.g.f.: (25 +231*x +121*x^2)*exp(x). (End)