A295853 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -2, a(1) = -1, a(2) = 2, a(3) = 1.

-2, -1, 2, 1, 13, 14, 47, 61, 148, 209, 437, 646, 1243, 1889, 3452, 5341, 9433, 14774, 25487, 40261, 68308, 108569, 181997, 290566, 482803, 773369, 1276652, 2050021, 3367633, 5417654, 8867207, 14284861, 23315908, 37600769, 61244357, 98845126, 160744843

Offset

0,1

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

G.f.: (-2 + x + 9 x^2 - 2 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).

Mathematica

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

Crossrefs

Cf. A001622, A000045.

Sequence in context: A134304 A211096 A134569 * A287541 A288196 A072883

Adjacent sequences: A295850 A295851 A295852 * A295854 A295855 A295856

Keyword

easy,sign

Author

Clark Kimberling, Dec 01 2017

Status

approved