A130195 Row sums of triangle A130194.

1, 3, 2, -2, -1, 5, 4, -4, -3, 7, 6, -6, -5, 9, 8, -8, -7, 11, 10, -10, -9, 13, 12, -12, -11, 15, 14, -14, -13, 17, 16, -16, -15, 19, 18, -18, -17, 21, 20, -20, -19, 23, 22, -22, -21, 25, 24, -24, -23, 27, 26, -26, -25, 29, 28, -28, -27, 31, 30, -30, -29, 33

Offset

1,2

Links

Table of n, a(n) for n=1..62.

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

Formula

Row sums of A130194, which is composed of A009531 in every column.

a(n) = a(n-1)-2*a(n-2)+2*a(n-3)-a(n-4)+a(n-5). - Colin Barker, Oct 03 2014

G.f.: -x*(x+1)^2/((x-1)*(x^2+1)^2). - Colin Barker, Oct 03 2014

a(n) = (4+(3+(2*n+1)*(-1)^n)*(-1)^((2*n-3-(-1)^n)/4))/4. - Luce ETIENNE, Aug 14 2015

Example

a(4) = -2 = sum of A130194 row 4 terms: (-4, -1, 2, 1).

Mathematica

LinearRecurrence[{1, -2, 2, -1, 1}, {1, 3, 2, -2, -1}, 70] (* Harvey P. Dale, Jun 24 2023 *)

Prog

(PARI) lista(nn) = {vgf = x*(1+x)^2/(1+x^2)^2 + O(x^(nn+1)); m = matrix(nn, nn, i, j, if (i >= j, polcoeff(vgf, i-j+1))); for (n=1, nn, s = sum(k=1, n, m[n, k]); print1(s, ", "); ); } \\ Michel Marcus, Oct 03 2014
(PARI) Vec(-x*(x+1)^2/((x-1)*(x^2+1)^2) + O(x^100)) \\ Colin Barker, Oct 03 2014

Crossrefs

Cf. A130194, A009531.

Sequence in context: A239067 A131015 A342769 * A071048 A357104 A098054

Adjacent sequences: A130192 A130193 A130194 * A130196 A130197 A130198

Keyword

sign,easy

Author

Gary W. Adamson, May 16 2007

Extensions

More terms from Michel Marcus, Oct 03 2014

Status

approved