A017078 a(n) = (8*n + 1)^2.

1, 81, 289, 625, 1089, 1681, 2401, 3249, 4225, 5329, 6561, 7921, 9409, 11025, 12769, 14641, 16641, 18769, 21025, 23409, 25921, 28561, 31329, 34225, 37249, 40401, 43681, 47089, 50625, 54289, 58081

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+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), this sequence (m=8), A017174 (m=9), A017282 (m=10), A017402 (m=11), A017534 (m=12), A134934 (m=14).

Programs

Magma

[(8*n+1)^2: n in [0..40]]; // Vincenzo Librandi, Jul 11 2011

Mathematica

(8*Range[0,40] +1)^2 (* G. C. Greubel, Dec 28 2022 *)

PARI

a(n)=(8*n+1)^2 \\ Charles R Greathouse IV, Jun 17 2017

SageMath

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

Formula

G.f.: (1 + 78*x + 49*x^2)/(1-x)^3. - R. J. Mathar, Mar 21 2016

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

a(2*n) = A016754(8*n).

E.g.f.: (1 + 80*x + 64*x^2)*exp(x). (End)

Sum_{n>=0} 1/a(n) = psi'(1/8)/64 = 1.02168958507793.. - R. J. Mathar, May 07 2024