A229204 For k>0, a(3k+1) = k*(k-3), a(3k+2) = k*(k-1), a(3k+3) = k*(k-1)-1.

0, 0, 0, -2, 0, -1, -2, 2, 1, 0, 6, 5, 4, 12, 11, 10, 20, 19, 18, 30, 29, 28, 42, 41, 40, 56, 55, 54, 72, 71, 70, 90, 89, 88, 110, 109, 108, 132, 131, 130, 156, 155, 154, 182, 181, 180, 210, 209, 208, 240, 239, 238, 272, 271, 270, 306, 305, 304, 342, 341

Offset

1,4

Comments

The first differences are 0, 0, -2, 2, -1, -1, 4, -1, -1, 6, -1, -1, 8, -1, -1, 10, ... .

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,2,-2,0,-1,1).

Formula

From Colin Barker, Jan 12 2016: (Start)

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

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

(End)

Prog

(Magma) &cat[IsZero(k) select [0, 0, 0] else [k*(k-3), k*(k-1), k*(k-1)-1]: k in [0..30]]; // Bruno Berselli, Sep 16 2013
(PARI) concat(vector(3), Vec(-x^4*(1+x^2)*(2-2*x-x^2-x^3+x^4)/((1-x)^3*(1+x+x^2)^2) + O(x^100))) \\ Colin Barker, Jan 12 2016

Crossrefs

Sequence in context: A316716 A145462 A159934 * A067460 A159855 A128256

Adjacent sequences: A229201 A229202 A229203 * A229205 A229206 A229207

Keyword

sign,easy

Author

Ralf Stephan, Sep 16 2013

Status

approved