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Search: id:A008934
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| A008934 |
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Number of tournament sequences: sequences (a_1, a_2, ..., a_n) with a_1 = 1 such that a_i < a_{i+1} <= 2*a_i for all i. |
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25
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| 1, 1, 2, 7, 41, 397, 6377, 171886, 7892642, 627340987, 87635138366, 21808110976027, 9780286524758582, 7981750158298108606, 11950197013167283686587, 33046443615914736611839942
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Also number of Meeussen sequences of length n (see the Cook-Kleber reference).
Column 1 of triangle A093729. Also generated by the iteration procedure that constructs triangle A093654. - Paul D. Hanna (pauldhanna(AT)juno.com), Apr 14 2004
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REFERENCES
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M. Torelli, Increasing integer sequences and Goldbach's conjecture, preprint, 1996.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..30
M. Cook and M. Kleber, Tournament sequences and Meeussen sequences, Electronic J. Comb. 7 (2000), #R44.
Index entries for sequences related to tournaments
E. Neuwirth, Computing tournament sequence numbers efficiently...
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FORMULA
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a(n) = A093729(n, 1). a(n) = A093655(2^n). - Paul D. Hanna (pauldhanna(AT)juno.com), Apr 14 2004
a(n) = A097710(n, 0). - Paul D. Hanna (pauldhanna(AT)juno.com), Aug 24 2004
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PROGRAM
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(PARI) {T(n, k)=if(n<0, 0, if(n==0, 1, if(k==0, 0, if(k<=n, T(n, k-1)-T(n-1, k)+T(n-1, 2*k-1)+T(n-1, 2*k), sum(j=1, n+1, (-1)^(j-1)*binomial(n+1, j)*T(n, k-j))))))} /*(Cook-Kleber)*/ a(n)=T(n, 1)
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CROSSREFS
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Cf. A058222, A058223.
Cf. A093729, A093655.
Forms column 0 of triangle A097710.
Sequence in context: A113144 A006846 A047864 this_sequence A084871 A122942 A109172
Adjacent sequences: A008931 A008932 A008933 this_sequence A008935 A008936 A008937
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KEYWORD
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nonn,nice,easy
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AUTHOR
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torelli(AT)hermes.mc.dsi.unimi.it (Mauro Torelli), Jeffrey Shallit (shallit(AT)graceland.uwaterloo.ca)
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