A137505 Inverse binomial transform of A007910.

1, 1, 0, 2, 0, 0, 4, -4, 4, 4, -12, 20, -12, -12, 52, -76, 52, 52, -204, 308, -204, -204, 820, -1228, 820, 820, -3276, 4916, -3276, -3276, 13108, -19660, 13108, 13108, -52428, 78644, -52428, -52428, 209716, -314572, 209716, 209716, -838860, 1258292, -838860, -838860, 3355444, -5033164, 3355444

Offset: 0

Author

Paul Curtz, Apr 23 2008

Keywords

• sign

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1,0,2).

Programs

Mathematica

LinearRecurrence[{-1,0,2},{1,1,0},50] (* Harvey P. Dale, Sep 17 2012 *)

Formula

Recurrence: a(n) = -a(n-1) + 2a(n-3), starting 1,1,0.

O.g.f.: (1+x)^2/((1-x)(1+2x+2x^2)). - R. J. Mathar, Jun 12 2008

a(4n) = a(4n+1) = (-1)^n*A109499(n). - Paul Curtz, Nov 01 2009

a(n) = (1/5) * (A137429(n-1) + 4) = A077973(n-2) + 2*A077973(n-1) + A077973(n). - Ralf Stephan, Aug 18 2013

Extensions

More terms from R. J. Mathar, Jun 12 2008