A295691 - OEIS

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A295691

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

2, 2, 2, 1, 5, 9, 12, 18, 32, 53, 83, 133, 218, 354, 570, 921, 1493, 2417, 3908, 6322, 10232, 16557, 26787, 43341, 70130, 113474, 183602, 297073, 480677, 777753, 1258428, 2036178, 3294608, 5330789, 8625395, 13956181, 22581578, 36537762, 59119338, 95657097

(list; graph; refs; listen; history; text; internal format)

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, 0, 1, 1)

FORMULA

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

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

MATHEMATICA