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A171621 Numerator of 1/4 - 1/n^2, each fourth term multiplied by 4. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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 *)

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

Sequence in context: A049457 A061037 A070262 * A084183 A099730 A072800

Adjacent sequences:  A171618 A171619 A171620 * A171622 A171623 A171624

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Dec 13 2009

STATUS

approved

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Last modified May 25 19:44 EDT 2019. Contains 323576 sequences. (Running on oeis4.)