A295688 - OEIS

A295688

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

2, 1, 0, 2, 5, 6, 8, 15, 26, 40, 63, 104, 170, 273, 440, 714, 1157, 1870, 3024, 4895, 7922, 12816, 20735, 33552, 54290, 87841, 142128, 229970, 372101, 602070, 974168, 1576239, 2550410, 4126648, 6677055, 10803704, 17480762, 28284465, 45765224, 74049690

(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) = 0, a(3) = 1.

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

MATHEMATICA