A295731 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -1, a(1) = -1, a(2) = 0, a(3) = 1.

-1, -1, 0, 1, 5, 10, 23, 41, 80, 137, 249, 418, 731, 1213, 2072, 3413, 5741, 9410, 15663, 25585, 42272, 68881, 113201, 184130, 301427, 489653, 799272, 1297117, 2112773, 3426274, 5571815, 9030857, 14668208, 23764601, 38563881, 62459554, 101285579, 164007277

Offset: 0

Author

Clark Kimberling, Nov 30 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, -1, 0, 1}, 100]

Formula

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

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