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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

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OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

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

MATHEMATICA

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

PROG

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

(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

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).

Sequence in context: A236868 A237375 A237368 * A359245 A236055 A236048

Adjacent sequences: A017075 A017076 A017077 * A017079 A017080 A017081

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

URL: https://oeis.org/A017078

⇱ A017078 - OEIS