A154627 Expansion of (1-5x)/(1-8x+4x^2).

1, 3, 20, 148, 1104, 8240, 61504, 459072, 3426560, 25576192, 190903296, 1424921600, 10635759616, 79386390528, 592548085760, 4422839123968, 33012520648704, 246408808693760, 1839220386955264, 13728127860867072

Offset: 0

Author

Paul Barry, Jan 13 2009

Keywords

• easy
• nonn

Comments

Hankel transform of 1,1,4,18,88,.... (see A081671).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-4).

Programs

Maple

A[0]:= 1: A[1]:= 3:
for n from 2 to 100 do A[n]:= 8*A[n-1]-4*A[n-2] od:
seq(A[n],n=0..100); # Robert Israel, Aug 10 2014

Mathematica

LinearRecurrence[{8,-4},{1,3},20] (* Harvey P. Dale, Aug 10 2014 *)
CoefficientList[Series[(1 - 5 x)/(1 - 8 x + 4 x^2), {x, 0, 50}], x] (* Vincenzo Librandi, Aug 10 2014 *)

PARI

Vec((1-5*x)/(1-8*x+4*x^2)+O(x^50)) \\ Michel Marcus, Aug 10 2014

Formula

a(n) = 8*a(n-1) - 4*a(n-2), n > 1; a(0)=1, a(1)=3. [Philippe Deléham, Feb 02 2009]