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

Author

Paul Curtz, Jan 13 2009

Keywords

• nonn
• easy
• mult

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).

Crossrefs

Cf. A000290, A016754, A022998, A061038.

Programs

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 *)

PARI

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

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

Extensions

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

a(0) added Oct 21 2009