A113312 Expansion of (1+x)^2/(1-2x^2+x^3).

1, 2, 3, 3, 4, 3, 5, 2, 7, -1, 12, -9, 25, -30, 59, -85, 148, -229, 381, -606, 991, -1593, 2588, -4177, 6769, -10942, 17715, -28653, 46372, -75021, 121397, -196414, 317815, -514225, 832044, -1346265, 2178313, -3524574, 5702891, -9227461, 14930356, -24157813, 39088173, -63245982, 102334159

Offset

0,2

Comments

Diagonal sums of A113310.

Links

Table of n, a(n) for n=0..44.

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

Formula

a(n)=2a(n-2)-a(n-3); a(n)=sum{k=0..floor(n/2), sum{i=0..n-2k, (-1)^i*C(i+k-2, i)}}.

Mathematica

LinearRecurrence[{0, 2, -1}, {1, 2, 3}, 50] (* Harvey P. Dale, May 19 2014 *)

Crossrefs

Sequence in context: A179846 A086925 A088858 * A334954 A053475 A140605

Adjacent sequences: A113309 A113310 A113311 * A113313 A113314 A113315

Keyword

easy,sign

Author

Paul Barry, Oct 25 2005

Status

approved