A136336 a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3) for n>3.

1, 2, 4, 7, 15, 27, 59, 107, 235, 427, 939, 1707, 3755, 6827, 15019, 27307, 60075, 109227, 240299, 436907, 961195, 1747627, 3844779, 6990507, 15379115, 27962027, 61516459, 111848107, 246065835, 447392427, 984263339, 1789569707, 3937053355, 7158278827

Offset: 0

Author

Paul Curtz, Mar 28 2008

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,4,-4).

Programs

Mathematica

LinearRecurrence[{1,4,-4},{1,2,4,7},50] (* Harvey P. Dale, Jan 14 2019 *)

PARI

Vec((1 + x - 2*x^2 - x^3) / ((1 - x)*(1 - 2*x)*(1 + 2*x)) + O(x^50)) \\ Colin Barker, Mar 17 2017

Formula

From Colin Barker, Mar 17 2017: (Start)

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

a(n) = (8 + (-2)^n + 21*2^n) / 24 for n>0.

(End)