A017402 a(n) = (11*n+1)^2.

1, 144, 529, 1156, 2025, 3136, 4489, 6084, 7921, 10000, 12321, 14884, 17689, 20736, 24025, 27556, 31329, 35344, 39601, 44100, 48841, 53824, 59049, 64516, 70225, 76176, 82369, 88804, 95481, 102400

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

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), this sequence (m=11), A017534 (m=12), A134934 (m=14).

Cf. A017534, A082043.

Programs

Magma

[(11*n+1)^2: n in [0..50]]; // G. C. Greubel, Dec 24 2022

Mathematica

(11*Range[0,30]+1)^2 (* or *) LinearRecurrence[{3,-3,1},{1,144,529},30] (* Harvey P. Dale, May 05 2014 *)

PARI

a(n)=(11*n+1)^2 \\ Charles R Greathouse IV, Jun 17 2017

SageMath

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

Formula

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, May 05 2014

From G. C. Greubel, Dec 24 2022: (Start)

G.f.: (1 + 141*x + 100*x^2)/(1-x)^3.

E.g.f.: (1 + 143*x + 121*x^2)*exp(x). (End)