A017534 a(n) = (12*n + 1)^2.

1, 169, 625, 1369, 2401, 3721, 5329, 7225, 9409, 11881, 14641, 17689, 21025, 24649, 28561, 32761, 37249, 42025, 47089, 52441, 58081, 64009, 70225, 76729, 83521, 90601, 97969, 105625, 113569, 121801

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Sequences of the form (m*n+1)^2: A000012 (m=0), A000290 (m=1), A016754 (m=2), A016778 (m=3), A016814 (m=4), A016862 (m=5), A016922 (m=6), A016994 (m=7), A017078 (m=8), A017174 (m=9), A017282 (m=10), A017402 (m=11), this sequence (m=12), A134934 (m=14).

Cf. A082043.

Programs

Magma

I:=[1, 169, 625]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jul 07 2012

Mathematica

CoefficientList[Series[(1+166*x+121*x^2)/(1-x)^3,{x,0,50}],x] (* Vincenzo Librandi, Jul 07 2012 *)
LinearRecurrence[{3,-3,1},{1,169,625},30] (* Harvey P. Dale, Feb 27 2023 *)

PARI

a(n)=(12*n+1)^2 \\ Charles R Greathouse IV, Jun 17 2017

SageMath

[(12*n+1)^2 for n in range(51)] # G. C. Greubel, Dec 24 2022

Formula

G.f.: (1 + 166*x + 121*x^2 )/(1-x)^3. - R. J. Mathar, Mar 10 2011

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jul 07 2012

E.g.f.: (1 + 168*x + 144*x^2)*exp(x). - G. C. Greubel, Dec 24 2022