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Search: id:A110914
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| A110914 |
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"Self convolution mod 3" of central Delannoy numbers (see comment). |
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+0
1
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| 1, 0, 2, 0, 1, 0, 2, 0, 4, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 4, 0, 2, 0, 4, 0, 8, 0, 4, 0, 2, 0, 4, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 4, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 4, 0, 2, 0, 4, 0, 8, 0, 4, 0, 2, 0, 4, 0, 2, 0, 4, 0, 8, 0, 4, 0, 8, 0, 16, 0, 8, 0, 4, 0, 8, 0, 4, 0, 2, 0, 4, 0, 2, 0, 4, 0, 8, 0, 4
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n)=sum(k=0,n,{b(k)*b(n-k)} mod 3) where b(k)=sum(k=0,n,binomial(n,k)*binomial(n+k,k)) are the central Delannoy numbers. The formula is obtained using techniques described in the Deutsch-Sagan paper.
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LINKS
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E. Deutsch and B. E. Sagan, Congruences for Catalan and Motzkin numbers and related sequences, J. Num. Theory 117 (2006), 191-215.
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FORMULA
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a(2n-1)=0 and a(2n)=2^t_1(n) where t_1(n) denotes the number of 1's in the ternary representation of n (A062756). Recurrence : a(3n)=a(n), a(3n+1)=a(n-1), a(3n+2)=2*a(n)
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PROGRAM
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(PARI) b(n)=sum(k=0, n, binomial(n, k)*binomial(n+k, k)); a(n)=sum(k=0, n, (b(k)*b(n-k))%3)
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CROSSREFS
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Cf. A062756.
Sequence in context: A054014 A158945 A156667 this_sequence A127505 A138036 A086372
Adjacent sequences: A110911 A110912 A110913 this_sequence A110915 A110916 A110917
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 04 2005
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