A111573 - OEIS

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A111573

a(n) = a(n-1) + a(n-3) + a(n-4), n >= 4.

0, 1, 3, 3, 4, 8, 14, 21, 33, 55, 90, 144, 232, 377, 611, 987, 1596, 2584, 4182, 6765, 10945, 17711, 28658, 46368, 75024, 121393, 196419, 317811, 514228, 832040, 1346270, 2178309, 3524577, 5702887, 9227466, 14930352, 24157816, 39088169

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

OFFSET

0,3

COMMENTS

See comment and FAMP code for A111569.

LINKS

Table of n, a(n) for n=0..37.

Index entries for linear recurrences with constant coefficients, signature (1,0,1,1).

FORMULA

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

a(n) = A056594(n+3) + A000045(n+1). - R. J. Mathar, Nov 10 2009

From Greg Dresden, Jan 15 2024: (Start)

a(2*n) = Fibonacci(n)*Lucas(n+1);

a(2*n+1) = Fibonacci(2*n+1). (End)

MATHEMATICA

Table[Fibonacci[n + 1] - Cos[n*Pi/2], {n, 0, 40}] (* Greg Dresden, Oct 16 2021 *)

CROSSREFS

Cf. A001638, A111569, A111570, A111571, A111572, A111574, A111575, A111576.

Sequence in context: A155822 A160646 A019466 * A049854 A353265 A366758

Adjacent sequences: A111570 A111571 A111572 * A111574 A111575 A111576

KEYWORD

easy,nonn

AUTHOR

Creighton Dement, Aug 10 2005

STATUS

approved