A099212 a(n) = -2*a(n-1) + 4*a(n-3), with a(0) = 1, a(1) = a(2) = 0.

1, 0, 0, 4, -8, 16, -16, 0, 64, -192, 384, -512, 256, 1024, -4096, 9216, -14336, 12288, 12288, -81920, 212992, -376832, 425984, 0, -1507328, 4718592, -9437184, 12845056, -6815744, -24117248, 99614720, -226492416, 356515840, -314572800, -276824064, 1979711488

Offset: 0

Author

Paul Barry, Oct 06 2004

Keywords

• easy
• sign

Comments

Binomial transform is A099213.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-2,0,4).

Crossrefs

Cf. A099211.

Programs

Mathematica

LinearRecurrence[{-2,0,4},{1,0,0},40] (* Harvey P. Dale, May 02 2019 *)

Formula

G.f.: (1 + 2*x)/(1 + 2*x - 4*x^3).

Extensions

a(31) onwards from Andrew Howroyd, Mar 19 2025