A017498 a(n) = (11*n + 9)^2.

81, 400, 961, 1764, 2809, 4096, 5625, 7396, 9409, 11664, 14161, 16900, 19881, 23104, 26569, 30276, 34225, 38416, 42849, 47524, 52441, 57600, 63001, 68644, 74529, 80656, 87025, 93636, 100489, 107584, 114921, 122500, 130321, 138384, 146689, 155236, 164025

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 (3,-3,1).

Crossrefs

Powers of the form (11*n+9)^m: A017497 (m=1), this sequence (m=2), A017499 (m=3), A017500 (m=4), A017501 (m=5), A017502 (m=6), A017503 (m=7), A017504 (m=8), A017505 (m=9), A017506 (m=10), A017607 (m=11), A017508 (m=12).

Programs

GAP

List([0..30], n-> (11*n+9)^2 ); # G. C. Greubel, Oct 28 2019

Magma

[(11*n+9)^2: n in [0..30]]; // G. C. Greubel, Oct 28 2019

Maple

seq((11*n+9)^2, n=0..30); # G. C. Greubel, Oct 28 2019

Mathematica

(11Range[0,30]+9)^2 (* or *) LinearRecurrence[{3,-3,1},{81,400,961},30] (* Harvey P. Dale, Oct 30 2011 *)

PARI

a(n)=(11*n+9)^2 \\ Charles R Greathouse IV, Jun 17 2017

Sage

[(11*n+9)^2 for n in (0..30)] # G. C. Greubel, Oct 28 2019

Formula

a(0)=81, a(1)=400, a(2)=961, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Oct 30 2011

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

G.f.: (81 + 157*x +4*x^2)/(1-x)^3.

E.g.f.: (81 + 319*x + 121*x^2)*exp(x). (End)