A295718 - OEIS

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A295718

a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = 3, a(2) = 4, a(3) = 5.

1, 3, 4, 5, 9, 10, 19, 21, 40, 45, 85, 98, 183, 217, 400, 489, 889, 1122, 2011, 2621, 4632, 6229, 10861, 15042, 25903, 36849, 62752, 91409, 154161, 229186, 383347, 579765, 963112, 1477341, 2440453, 3786722, 6227175, 9751753, 15978928, 25206393, 41185321

(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 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, 3, -2, -2)

FORMULA

a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 3, a(2) = 4, a(3) = 5.

G.f.: (1 + 2 x - 2 x^2 - 6 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).

MATHEMATICA