A295719 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = 3, a(2) = 6, a(3) = 10.

1, 3, 6, 10, 20, 32, 60, 96, 172, 276, 480, 772, 1316, 2120, 3564, 5748, 9568, 15444, 25524, 41224, 67772, 109508, 179328, 289860, 473284, 765192, 1246668, 2015956, 3279008, 5303156, 8614932, 13934472, 22614940, 36582180, 59328192, 95975908, 155566244

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}, {1, 3, 6, 10}, 100]

Formula

a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 3, a(2) = 6, a(3) = 10.

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