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A111573 a(n) = a(n-1) + a(n-3) + a(n-4), 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 (list; graph; refs; listen; history; text; internal format)
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+x-1)*(x^2+1))

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

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 A195978 A197280

Adjacent sequences:  A111570 A111571 A111572 * A111574 A111575 A111576

KEYWORD

easy,nonn

AUTHOR

Creighton Dement, Aug 10 2005

STATUS

approved

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Last modified June 25 06:13 EDT 2017. Contains 288709 sequences.