A114220 a(n) = Sum_{k=0..floor(n/2)} k-(k-1)*0^(n-2k).

1, 0, 1, 1, 2, 3, 4, 6, 7, 10, 11, 15, 16, 21, 22, 28, 29, 36, 37, 45, 46, 55, 56, 66, 67, 78, 79, 91, 92, 105, 106, 120, 121, 136, 137, 153, 154, 171, 172, 190, 191, 210, 211, 231, 232, 253, 254, 276, 277, 300, 301, 325, 326, 351, 352, 378, 379, 406, 407, 435, 436

Offset

0,5

Comments

Diagonal sums of A114219.

Links

Table of n, a(n) for n=0..60.

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

Formula

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

a(n) = a(n-1)+2a(n-2)-2a(n-3)-a(n-4)+a(n-5).

a(n) = (2n^2-2n+7)/16+(9-2n)(-1)^n/16.

a(n) = A055802(n+1), n > 1. - R. J. Mathar, Aug 11 2008

Mathematica

CoefficientList[Series[(1-x-x^2+2x^3)/((1-x)(1-x^2)^2), {x, 0, 80}], x] (* Harvey P. Dale, Mar 24 2011 *)

Crossrefs

Cf. A114219.

Column k=2 of A309049 (for n>0).

Sequence in context: A049995 A294848 A055802 * A134519 A101505 A259625

Adjacent sequences: A114217 A114218 A114219 * A114221 A114222 A114223

Keyword

easy,nonn

Author

Paul Barry, Nov 18 2005

Status

approved