A295723 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = 1, a(2) = 2, a(3) = 3.

0, 1, 2, 3, 7, 10, 21, 31, 60, 91, 167, 258, 457, 715, 1236, 1951, 3315, 5266, 8837, 14103, 23452, 37555, 62031, 99586, 163665, 263251, 431012, 694263, 1133467, 1827730, 2977581, 4805311, 7815660, 12620971, 20502167, 33123138, 53756377, 86879515, 140898036

Offset: 0

Author

Clark Kimberling, Nov 29 2017

Keywords

• nonn
• easy

Comments

a(n)/a(n-1) -> (1 + sqrt(5))/2 = golden ratio (A001622), so that a( ) has the growth rate of the Fibonacci numbers (A000045).

Links

• Clark Kimberling, Table of n, a(n) for n = 0..2000
• Index entries for linear recurrences with constant coefficients, signature (1, 3, -2, -2)

Crossrefs

Cf. A001622, A000045, A005672.

Programs

Mathematica

LinearRecurrence[{1, 3, -2, -2}, {0, 1, 2, 3}, 100]

Formula

a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 0, a(1) = 1, a(2) = 2, a(3) = 3.

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