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Search: id:A111573
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| A111573 |
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a(n) = a(n-1) + a(n-3) + a(n-4), n >= 4. |
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+0
6
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| 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; listen)
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OFFSET
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0,3
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COMMENT
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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 (jvospost3(AT)gmail.com), Aug 10 2005
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FORMULA
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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 (mathar(AT)strw.leidenuniv.nl), Nov 10 2009]
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PROGRAM
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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
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CROSSREFS
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Cf. A001638, A111569, A111570, A111571, A111572, A111574, A111575, A111576.
Sequence in context: A155822 A160646 A019466 this_sequence A049854 A086239 A016605
Adjacent sequences: A111570 A111571 A111572 this_sequence A111574 A111575 A111576
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KEYWORD
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easy,nonn,new
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AUTHOR
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Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Aug 10 2005
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