A089979 Expansion of 1/(1-4x-4x^3).

1, 4, 16, 68, 288, 1216, 5136, 21696, 91648, 387136, 1635328, 6907904, 29180160, 123261952, 520679424, 2199438336, 9290801152, 39245922304, 165781442560, 700288974848, 2958139588608, 12495684124672, 52783892398080

Offset: 0

Author

Paul Barry, Nov 18 2003

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,0,4).

Crossrefs

Cf. A052912, A000930, A089978.

Programs

Mathematica

CoefficientList[Series[1/(1 - 4*x - 4*x^3), {x, 0, 50}], x] (* or *) LinearRecurrence[{4,0,4}, {1,4,16}, 50] (* G. C. Greubel, Apr 29 2017 *)

PARI

x='x+O('x^50); Vec(1/(1 - 4*x - 4*x^3)) \\ G. C. Greubel, Apr 29 2017

Formula

a(n) = Sum_{k=0..floor(n/2)} C(n-2*k, k)*4^(n-2*k).

a(n) = 4*a(n-1) + 4*a(n-3). - G. C. Greubel, Apr 29 2017