A130507 First differences of A130845.

0, 0, 1, 0, 0, 0, 2, -1, 0, 0, 3, -2, 0, 0, 4, -3, 0, 0, 5, -4, 0, 0, 6, -5, 0, 0, 7, -6, 0, 0, 8, -7, 0, 0, 9, -8, 0, 0, 10, -9, 0, 0, 11, -10, 0, 0, 12, -11, 0, 0, 13, -12, 0, 0, 14, -13, 0, 0, 15, -14, 0, 0, 16, -15, 0, 0, 17, -16, 0, 0, 18, -17, 0, 0, 19, -18, 0, 0, 20, -19, 0, 0, 21, -20, 0, 0, 22, -21, 0, 0, 23, -22, 0, 0, 24, -23, 0, 0, 25, -24, 0

Offset: 0

Author

Paul Curtz, Aug 16 2007

Keywords

• sign
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1,-1,-1,1,1,1,1).

Crossrefs

Cf. A130845.

Programs

PARI

concat(vector(2), Vec(x^2*(1 + x + x^2 + x^3 + x^4) / ((1 - x)*(1 + x)^2*(1 + x^2)^2) + O(x^100))) \\ Colin Barker, Sep 25 2017

Formula

a(n) = (1/16)*(cos(n*Pi/2)+sin(n*Pi/2)-1)*((2n-1)*cos(n*Pi/2)-5*cos(n*Pi)+(2n-1)*sin(n*Pi/2))*(-1)^floor((n-1)/2). - Wesley Ivan Hurt, Sep 24 2017

From Colin Barker, Sep 25 2017: (Start)

G.f.: x^2*(1 + x + x^2 + x^3 + x^4) / ((1 - x)*(1 + x)^2*(1 + x^2)^2).

a(n) = -a(n-1) - a(n-2) - a(n-3) + a(n-4) + a(n-5) + a(n-6) + a(n-7) for n>6.

(End)

Extensions

One term corrected by Colin Barker, Sep 25 2017