

A111573


a(n) = a(n1) + a(n3) + a(n4), n >= 4.


6



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
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OFFSET

0,3


COMMENTS

See comment and FAMP code for A111569.
Many of these are also Fibonacci numbers (A000045), including 1, 3, 8, 21, 55, 144, 377, 987, 2584, 6765, 17711, 46368, 121393, 317811, 832040, ... and many differ from a Fibonacci number by 1. Why? a(30) and a(31) are both divisible by 2207. Similarly, a(32) and a(33) are both divisible by 3571. Why?  Jonathan Vos Post, Aug 10 2005


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+x1)*(x^2+1))
a(n) = A056594(n+3)+A000045(n+1). [R. J. Mathar, Nov 10 2009]


MATHEMATICA

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


PROG

Floretion Algebra Multiplication Program, FAMP Code: 2kbaseseq[B+H] with B =  .25'i + .25'j  .25i' + .25j' + k'  .5'kk'  .25'ik'  .25'jk'  .25'ki'  .25'kj'  .5e and H = + .75'ii' + .75'jj' + .75'kk' + .75e


CROSSREFS

Cf. A001638, A111569, A111570, A111571, A111572, A111574, A111575, A111576.
Sequence in context: A155822 A160646 A019466 * A049854 A353265 A291872
Adjacent sequences: A111570 A111571 A111572 * A111574 A111575 A111576


KEYWORD

easy,nonn


AUTHOR

Creighton Dement, Aug 10 2005


STATUS

approved



