A147560 a(n) = 4*A046162(n+1).

0, 4, 16, 12, 64, 100, 48, 196, 256, 108, 400, 484, 192, 676, 784, 300, 1024, 1156, 432, 1444, 1600, 588, 1936, 2116, 768, 2500, 2704, 972, 3136, 3364, 1200, 3844, 4096, 1452, 4624, 4900, 1728, 5476, 5776, 2028, 6400, 6724, 2352, 7396, 7744, 2700, 8464

Offset

0,2

Links

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

Formula

a(n) = 4*numerator(n^2/(n^2 + 3*n + 3)).

Sum_{n>=1} 1/a(n) = 11*Pi^2/216. - Amiram Eldar, Aug 14 2022

G.f.: 4*x*(1 + 4*x + 3*x^2 + 13*x^3 + 13*x^4 + 3*x^5 + 4*x^6 + x^7)/(1-x^3)^3. - G. C. Greubel, Oct 27 2022

Maple

A046162 := proc(n) (n-1)^2/(n^2+n+1) ; numer(%) ; end proc: A147560 := proc(n) 4*A046162(n+1) ; end proc: seq(A147560(n), n=0..70) ; # R. J. Mathar, Dec 15 2009

Mathematica

a[n_] := 4 * Numerator[n^2/(n^2 + 3*n + 3)]; Array[a, 50, 0] (* Amiram Eldar, Aug 14 2022 *)

Prog

(Magma) [4*Numerator(n^2/(n^2+3*n+3)): n in [0..70]]; // G. C. Greubel, Oct 27 2022
(SageMath) [4*numerator(n^2/(n^2 +3*n +3)) for n in range(71)] # G. C. Greubel, Oct 27 2022

Crossrefs

Companion to A144437.

Cf. A046162.

Cf. A171522. [R. J. Mathar, Dec 15 2009]

Sequence in context: A223987 A224123 A273579 * A266973 A029659 A265218

Adjacent sequences: A147557 A147558 A147559 * A147561 A147562 A147563

Keyword

nonn,easy,less

Author

Paul Curtz, Nov 07 2008

Extensions

More terms from R. J. Mathar, Dec 15 2009

Status

approved