A088013 Binomial transform of A001541 (with interpolated zeros).

1, 1, 4, 10, 36, 116, 400, 1352, 4624, 15760, 53824, 183712, 627264, 2141504, 7311616, 24963200, 85229824, 290992384, 993510400, 3392055808, 11581203456, 39540700160, 135000395776, 460920178688, 1573679927296, 5372879343616

Offset: 0

Author

Paul Barry, Sep 18 2003

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (4,0,-8,4).

Programs

Mathematica

LinearRecurrence[{4,0,-8,4},{1,1,4,10},30] (* Harvey P. Dale, Jun 16 2017 *)

Formula

G.f.: (1-3x+2x^3)/(1-4x+8x^3-4x^4);

e.g.f.: exp(x)cosh(x)cosh(sqrt(2)x);

a(n) = ((sqrt(2))^n + (-sqrt(2))^n + (2+sqrt(2))^n + (2-sqrt(2))^n)/4.