A295852 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) = 2, a(3) = 1.

-1, -1, 2, 1, 11, 12, 39, 51, 122, 173, 359, 532, 1019, 1551, 2826, 4377, 7715, 12092, 20831, 32923, 55802, 88725, 148623, 237348, 394163, 631511, 1042058, 1673569, 2748395, 4421964, 7235895, 11657859, 19024826, 30682685, 49969655, 80652340, 131146283

Offset

0,3

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)

Formula

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

G.f.: (-1 + 6 x^2)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).

Mathematica

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

Crossrefs

Cf. A001622, A000045.

Sequence in context: A308846 A038586 A140316 * A088587 A305711 A158352

Adjacent sequences: A295849 A295850 A295851 * A295853 A295854 A295855

Keyword

easy,sign

Author

Clark Kimberling, Dec 01 2017

Status

approved