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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. 5
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 a( ) 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 + x^3 + x^4).

MATHEMATICA

LinearRecurrence[{1, 0, 1, 1}, {1, 2, 3, 4}, 100]

CROSSREFS

Cf. A001622, A000045, A295619, A295620.

Sequence in context: A228494 A292324 A289919 * A227047 A298304 A307970

Adjacent sequences:  A293408 A293409 A293410 * A293412 A293413 A293414

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Nov 25 2017

STATUS

approved

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Last modified August 2 15:15 EDT 2021. Contains 346428 sequences. (Running on oeis4.)