A295721 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -1, a(1) = 2, a(2) = 3, a(3) = 4.

-1, 2, 3, 4, 11, 13, 32, 41, 89, 122, 243, 349, 656, 973, 1757, 2666, 4679, 7217, 12408, 19369, 32801, 51658, 86507, 137141, 227744, 362837, 598773, 957514, 1572671, 2521993, 4127432, 6633041, 10826009, 17426282, 28383363, 45744109, 74389616, 120002653

Offset: 0

Author

Clark Kimberling, Nov 29 2017

Keywords

• easy
• sign

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, 2, 3, 4}, 100]

Formula

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

G.f.: (-1 + 3 x + 4 x^2 - 7 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).