A295855 - OEIS

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

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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