A017438 a(n) = (11*n + 4)^2.

16, 225, 676, 1369, 2304, 3481, 4900, 6561, 8464, 10609, 12996, 15625, 18496, 21609, 24964, 28561, 32400, 36481, 40804, 45369, 50176, 55225, 60516, 66049, 71824, 77841, 84100, 90601, 97344, 104329, 111556, 119025, 126736, 134689, 142884, 151321, 160000, 168921, 178084, 187489, 197136

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+4)^m: A017437 (m=1), this sequence (m=2), A017439 (m=3), A017440 (m=4), A017441 (m=5), A017442 (m=6), A017443 (m=7), A017444 (m=8), A017445 (m=9), A017446 (m=10), A017447 (m=11), A017448 (m=12).

Programs

GAP

List([0..50], n-> (11*n+4)^2); # G. C. Greubel, Sep 18 2019

Magma

[(11*n+4)^2: n in [0..50]]; // G. C. Greubel, Sep 18 2019

Maple

seq((11*n+4)^2, n=0..50); # G. C. Greubel, Sep 18 2019

Mathematica

(11*Range[50] -7)^2 (* G. C. Greubel, Sep 18 2019 *)

PARI

a(n)=(11*n+4)^2 \\ Charles R Greathouse IV, Jun 17 2017

Sage

[(11*n+4)^2 for n in (0..50)] # G. C. Greubel, Sep 18 2019

Formula

From Chai Wah Wu, Jul 10 2016: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.

G.f.: (49*x^2 + 177*x + 16)/(1 - x)^3. (End)

E.g.f.: (16 + 209*x + 121*x^2)*exp(x). - G. C. Greubel, Sep 18 2019

Extensions

Terms a(30) onward added by G. C. Greubel, Sep 18 2019