A295685 - OEIS

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A295685

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

2, 1, 1, 1, 4, 6, 8, 13, 23, 37, 58, 94, 154, 249, 401, 649, 1052, 1702, 2752, 4453, 7207, 11661, 18866, 30526, 49394, 79921, 129313, 209233, 338548, 547782, 886328, 1434109, 2320439, 3754549, 6074986, 9829534, 15904522, 25734057, 41638577, 67372633

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

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

MATHEMATICA