A295855 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) = 2, a(3) = 1.

1, -2, 2, 1, 9, 12, 33, 49, 106, 163, 317, 496, 909, 1437, 2538, 4039, 6961, 11128, 18857, 30241, 50634, 81387, 135093, 217504, 358741, 578293, 949322, 1531711, 2505609, 4045512, 6600273, 10662169, 17360746, 28055683, 45613037, 73734256, 119740509, 193605837

Offset

0,2

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

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

Mathematica

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

Crossrefs

Cf. A001622, A000045.

Sequence in context: A136730 A175714 A291082 * A364371 A285068 A306149

Adjacent sequences: A295852 A295853 A295854 * A295856 A295857 A295858

Keyword

easy,sign

Author

Clark Kimberling, Dec 01 2017

Status

approved