A154615 a(n) = A022998(n)^2.

0, 1, 16, 9, 64, 25, 144, 49, 256, 81, 400, 121, 576, 169, 784, 225, 1024, 289, 1296, 361, 1600, 441, 1936, 529, 2304, 625, 2704, 729, 3136, 841, 3600, 961, 4096, 1089, 4624, 1225, 5184, 1369, 5776, 1521, 6400, 1681, 7056, 1849, 7744, 2025, 8464, 2209, 9216

Offset

0,3

Comments

Multiplicative because A022998 is. - Andrew Howroyd, Jul 25 2018

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

Formula

Denominators of 1/4 - 1/(2n)^2, if n>0.

a(2n+1) = A016754(n). a(2n) = 16*A000290(n).

a(n) = A061038(2*n) (bisection).

a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6).

G.f.: x*(1+16*x+6*x^2+16*x^3+x^4)/((1-x)^3*(1+x)^3).

From G. C. Greubel, Jul 20 2017: (Start)

a(n) = (1/2)*(5 + 3*(-1)^n)*n^2.

E.g.f.: x*( (4*x +1)*cosh(x) + (x+4)*sinh(x) ). (End)

Sum_{n>=1} 1/a(n) = 13*Pi^2/96. - Amiram Eldar, Aug 13 2022

Mathematica

Join[{0}, Denominator[Table[(1/4)*(1 - 1/n^2), {n, 1, 50}]]] (* or *) Table[(1/2)*(5 + 3*(-1)^n)*n^2 {n, 0, 50}] (* G. C. Greubel, Jul 20 2017 *)

Prog

(PARI) for(n=0, 50, print1((1/2)*(5 + 3*(-1)^n)*n^2, ", ")) \\ G. C. Greubel, Jul 20 2017

Crossrefs

Cf. A000290, A016754, A022998, A061038.

Sequence in context: A281719 A103167 A303317 * A040242 A306378 A232999

Adjacent sequences: A154612 A154613 A154614 * A154616 A154617 A154618

Keyword

nonn,easy,mult

Author

Paul Curtz, Jan 13 2009

Extensions

Edited, offset set to 1, and extended by R. J. Mathar, Sep 07 2009

a(0) added Oct 21 2009

Status

approved