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URL: https://oeis.org/A154615

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A154615
a(n) = A022998(n)^2.
6
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
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
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