A293411 - OEIS

A293411

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

1, 2, 3, 4, 7, 12, 19, 30, 49, 80, 129, 208, 337, 546, 883, 1428, 2311, 3740, 6051, 9790, 15841, 25632, 41473, 67104, 108577, 175682, 284259, 459940, 744199, 1204140, 1948339, 3152478, 5100817, 8253296, 13354113, 21607408, 34961521, 56568930, 91530451

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

OFFSET

0,2

COMMENTS

a(n)/a(n-1) -> (1 + sqrt(5))/2 = golden ratio (A001622), so that this sequence has the growth rate of the Fibonacci numbers (A000045).

LINKS

Clark Kimberling, Table of n, a(n) for n = 0..1999

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) = 1, a(1) = 2, a(2) = 3, a(3) = 4.

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

From Greg Dresden, Aug 25 2021: (Start)