A016862 a(n) = (5*n + 1)^2.

1, 36, 121, 256, 441, 676, 961, 1296, 1681, 2116, 2601, 3136, 3721, 4356, 5041, 5776, 6561, 7396, 8281, 9216, 10201, 11236, 12321, 13456, 14641, 15876, 17161, 18496, 19881, 21316, 22801, 24336, 25921

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..200
• Eric Weisstein's World of Mathematics, Polygamma Function.
• Wikipedia, Polygamma Function.
• 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), this sequence (m=5), A016922 (m=6), A016994 (m=7), A017078 (m=8), A017174 (m=9), A017282 (m=10), A017402 (m=11), A017534 (m=12), A134934 (m=14).

Programs

Magma

[(5*n+1)^2: n in [0..40]]; // G. C. Greubel, Dec 28 2022

Mathematica

(5*Range[0,40]+1)^2 (* or *) LinearRecurrence[{3,-3,1},{1,36,121},40] (* Harvey P. Dale, Jul 11 2012 *)

PARI

a(n)=(5*n+1)^2 \\ Charles R Greathouse IV, Jun 17 2017

SageMath

[(5*n+1)^2 for n in range(41)] # G. C. Greubel, Dec 28 2022

Formula

a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Harvey P. Dale, Jul 11 2012

Sum_{n>=0} 1/a(n) = polygamma(1, 1/5)/25 = 1.050695088216... - Amiram Eldar, Oct 02 2020

G.f.: (1 +33*x +16*x^2)/(1-x)^3. - Wesley Ivan Hurt, Oct 02 2020

From G. C. Greubel, Dec 28 2022: (Start)

a(2*n) = A017282(n).

a(2*n+1) = 4*A016886(n).

E.g.f.: (1 + 35*x + 25*x^2)*exp(x). (End)