A131118 a(4n) = -n^2, a(4n+1) = n^2, a(4n+2) = 1-n^2, a(4n+3) = n*(n+1).

0, 0, 1, 0, -1, 1, 0, 2, -4, 4, -3, 6, -9, 9, -8, 12, -16, 16, -15, 20, -25, 25, -24, 30, -36, 36, -35, 42, -49, 49, -48, 56, -64, 64, -63, 72, -81, 81, -80, 90, -100, 100, -99, 110, -121, 121, -120, 132, -144, 144, -143, 156, -169, 169, -168

Offset: 0

Author

Paul Curtz, Sep 24 2007

Keywords

• sign
• easy

Comments

Up to signs, the first differences are in A131804. - R. J. Mathar, Mar 17 2009

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Programs

GAP

List([0..60], n-> ((7+4*n-2*n^2)*(-1)^n -2*((n+4)+(n+2)*(-1)^n)*(-1)^Binomial(n+1,2) +5)/32 ); # G. C. Greubel, Nov 18 2019

Magma

[((7+4*n-2*n^2)*(-1)^n -2*((n+4)+(n+2)*(-1)^n)*(-1)^Binomial(n+1,2) +5)/32: n in [0..60]]; // G. C. Greubel, Nov 18 2019

Maple

seq(((7+4*n-2*n^2)*(-1)^n -2*((n+4)+(n+2)*(-1)^n)*(-1)^binomial(n+1,2) +5)/32, n=0..60); # G. C. Greubel, Nov 18 2019

Mathematica

Table[((7+4*n-2*n^2)*(-1)^n -2*((n+4)+(n+2)*(-1)^n)*(-1)^Binomial[n+1,2] +5)/32, {n,0,60}] (* G. C. Greubel, Nov 18 2019 *)

PARI

a(n) = ((7+4*n-2*n^2)*(-1)^n -2*((n+4)+(n+2)*(-1)^n)*(-1)^binomial(n+1,2) +5)/32; \\ G. C. Greubel, Nov 18 2019

Sage

[((7+4*n-2*n^2)*(-1)^n -2*((n+4)+(n+2)*(-1)^n)*(-1)^binomial(n+1,2) +5)/32 for n in (0..60)] # G. C. Greubel, Nov 18 2019

Formula

From R. J. Mathar, Mar 17 2009: (Start)

a(n) = -2*a(n-1) -2*a(n-2) -2*a(n-3) +2*a(n-5) +2*a(n-6) +2*a(n-7) +a(n-8).

G.f.: x^2*(1+x^2+x^3+2*x)/((1-x)*(1+x^2)^2*(1+x)^3). (End)

a(n) = ((-2*n^2+4*n+7)*(-1)^n - 2*((n+4)+(n+2)*(-1)^n)*i^(n*(n+1))+5)/32, where i=sqrt(-1). - Bruno Berselli, Mar 27 2012

Extensions

More terms from Sean A. Irvine, Mar 13 2011