A171621 Numerator of 1/4 - 1/n^2, each fourth term multiplied by 4.

0, 5, 3, 21, 8, 45, 15, 77, 24, 117, 35, 165, 48, 221, 63, 285, 80, 357, 99, 437, 120, 525, 143, 621, 168, 725, 195, 837, 224, 957, 255, 1085, 288, 1221, 323, 1365, 360, 1517, 399, 1677, 440, 1845, 483, 2021, 528

Offset

2,2

Comments

These are the square roots of the fifth column of the array of denominators mentioned in A171522.

Links

Colin Barker, Table of n, a(n) for n = 2..1000

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

Formula

a(n) = A061037(n) * A010121(n+2).

a(2n+2) = A005563(n). a(2n+3) = A078371(n).

G.f.: x^3*(-5-3*x-6*x^2+x^3+3*x^4) / ( (x-1)^3*(1+x)^3 ). - R. J. Mathar, Apr 02 2011

a(n) = -(-5+3*(-1)^n)*(-4+n^2)/8. - Colin Barker, Nov 03 2014

Sum_{n>=3} 1/a(n) = 13/12. - Amiram Eldar, Aug 11 2022

Maple

A061037 := proc(n) 1/4-1/n^2 ; numer(%) ; end proc:
A171621 := proc(n) if n mod 4 = 2 then 4*A061037(n) ; else A061037(n) ; end if; end proc:
seq(A171621(n), n=2..90) ; # R. J. Mathar, Apr 02 2011

Mathematica

Table[-(-5+3*(-1)^n)*(-4+n^2)/8, {n, 0, 100}] (* G. C. Greubel, Sep 19 2018 *)
LinearRecurrence[{0, 3, 0, -3, 0, 1}, {0, 5, 3, 21, 8, 45}, 50] (* Harvey P. Dale, Nov 01 2019 *)

Prog

(PARI) concat(0, Vec(x^3*(-5-3*x-6*x^2+x^3+3*x^4)/((x-1)^3*(1+x)^3) + O(x^100))) \\ Colin Barker, Nov 03 2014
(Magma) [-(-5+3*(-1)^n)*(-4+n^2)/8: n in [0..100]]; // G. C. Greubel, Sep 19 2018

Crossrefs

Cf. A005563, A010121, A061037, A078371, A171522.

Sequence in context: A061037 A070262 A372289 * A084183 A099730 A072800

Adjacent sequences: A171618 A171619 A171620 * A171622 A171623 A171624

Keyword

nonn,easy

Author

Paul Curtz, Dec 13 2009

Status

approved