A038989 Expansion of (1 - x^2 - 2*x^3) / (1 - 2*x - 2*x^2 - 2*x^3 + x^4).

1, 2, 5, 14, 41, 118, 341, 986, 2849, 8234, 23797, 68774, 198761, 574430, 1660133, 4797874, 13866113, 40073810, 115815461, 334712894, 967338217, 2795659334, 8079605429, 23350493066, 67484177441, 195032892538, 563655520661, 1628994688214, 4707882025385

Offset: 0

Author

Colin Mallows

Keywords

• nonn
• easy

Links

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

Programs

GAP

a:=[1,2,5,14];; for n in [5..30] do a[n]:=2*a[n-1]+2*a[n-2]+2*a[n-3]-a[n-4]; od; a; # Muniru A Asiru, Sep 12 2018

Maple

seq(coeff(series((1-x^2-2*x^3)/(1-2*x-2*x^2-2*x^3+x^4),x,n+1), x, n), n = 0 .. 30); # Muniru A Asiru, Sep 12 2018

PARI

Vec((1 - x^2 - 2*x^3) / (1 - 2*x - 2*x^2 - 2*x^3 + x^4) + O(x^30)) \\ Colin Barker, Jul 16 2017

Formula

a(n) = 2*a(n-1) + 2*a(n-2) + 2*a(n-3) - a(n-4) for n>3. - Colin Barker, Jul 16 2017

Lim_{n -> inf} a(n)/a(n-1) = A318605. - A.H.M. Smeets, Sep 12 2018