A017222 a(n) = (9*n + 5)^2.

25, 196, 529, 1024, 1681, 2500, 3481, 4624, 5929, 7396, 9025, 10816, 12769, 14884, 17161, 19600, 22201, 24964, 27889, 30976, 34225, 37636, 41209, 44944, 48841, 52900, 57121, 61504, 66049, 70756

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

Sequences of the form (m*n+5)^2: A010864 (m=0), A000290 (m=1), A016754 (m=2), A016790 (m=3), A016814 (m=4), A016850 (m=5), A016970 (m=6), A017042 (m=7), A017126 (m=8), this sequence (m=9), A017330 (m=10), A017450 (m=11), A017582 (m=12).

Cf. A017221, A017246.

Programs

Magma

[(9*n+5)^2: n in [0..35]]; // Vincenzo Librandi, Jul 24 2011

Mathematica

(9Range[0,30]+5)^2 (* or *) LinearRecurrence[{3,-3,1},{25,196,529},30] (* Harvey P. Dale, May 22 2012 *)

PARI

a(n)=(9*n+5)^2 \\ Charles R Greathouse IV, Jun 17 2017

SageMath

[(9*n+5)^2 for n in range(41)] # G. C. Greubel, Dec 29 2022

Formula

a(n) = A017221(n)^2.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, May 22 2012

G.f.: (25 + 121*x + 16*x^2)/(1-x)^3. - R. J. Mathar, Mar 20 2018

From G. C. Greubel, Dec 29 2022: (Start)

a(2*n+1) = 4*A017246(n).

a(n) = a(n-1) + 9*(18*n + 1).

E.g.f.: (25 + 171*x + 81*x^2)*exp(x). (End)