A128498 Fourth column (m=3) of triangle A128494.

1, 1, -3, -3, 7, 7, -13, -13, 22, 22, -34, -34, 50, 50, -70, -70, 95, 95, -125, -125, 161, 161, -203, -203, 252, 252, -308, -308, 372, 372, -444, -444, 525, 525, -615, -615, 715, 715, -825, -825, 946, 946, -1078, -1078, 1222, 1222, -1378, -1378, 1547, 1547, -1729, -1729, 1925, 1925, -2135, -2135

Offset: 0

Author

Wolfdieter Lang, Apr 04 2007

Keywords

• sign
• easy

Comments

Unsigned, this is the repeated sequence A002623.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,-4,4,-6,6,-4,4,-1,1).

Crossrefs

Cf. A008642 (unsigned column m=2). A128499 (column m=4).

Programs

Mathematica

CoefficientList[Series[1/((1-x)(1+x^2)^4),{x,0,60}],x] (* or *) LinearRecurrence[{1,-4,4,-6,6,-4,4,-1,1},{1,1,-3,-3,7,7,-13,-13,22},60] (* Harvey P. Dale, Jul 04 2021 *)

PARI

Vec(1/((1-x)*(1+x^2)^4) + O(x^50)) \\ Michel Marcus, Mar 16 2015

Formula

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

a(2*k) = a(2*k+1)= ((-1)^k)*A002623(n), k>=0.

a(n) = (-1)^((2*n-1+(-1)^n)/4)*((n+2)*(n+7)*(2*n+9)+3*(n+3)*(n+6)*(-1)^n+12*(-1)^((2*n-1+(-1)^n)/4))/192. - Luce ETIENNE, Mar 13 2015