A295682 - OEIS

A295682

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

0, 2, 0, 1, 3, 5, 6, 10, 18, 29, 45, 73, 120, 194, 312, 505, 819, 1325, 2142, 3466, 5610, 9077, 14685, 23761, 38448, 62210, 100656, 162865, 263523, 426389, 689910, 1116298, 1806210, 2922509, 4728717, 7651225, 12379944, 20031170, 32411112, 52442281, 84853395

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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, 0, 1, 1)

FORMULA

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

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

MATHEMATICA