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Search: id:A091714
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| A091714 |
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Row sums of triangle A052313, which is the matrix square of the triangle of circular binomial coefficients (A047996). |
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1
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| 1, 3, 6, 10, 19, 31, 68, 120, 271, 567, 1302, 2918, 7199, 17071, 43110, 108642, 280935, 727959, 1930344, 5115348, 13765415, 37132859, 101046712, 275870592, 758236999, 2088996227, 5783712268, 16055661688, 44729027703, 124907034471
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Row sums of A047996 gives the number of n-bead necklaces with 2 colors when turning over is not allowed (A000031). This sequence may be regarded as the "circular binomial transform" of A000031.
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FORMULA
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a(n) = sum_{k=0..n} A047996(n, k)*A000031(k).
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PROGRAM
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(PARI) {A047996(n, k)=if(n<0|k>n, 0, if(n==0|k==0, 1, (1/n)*sumdiv(gcd(n, k), d, eulerphi(d)*binomial(n/d, k/d))))} a(n)=sum(k=0, n, A047996(n, k)*sum(j=0, k, A047996(k, j)))
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CROSSREFS
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Cf. A052313, A047996, A000031.
Sequence in context: A075111 A080014 A132274 this_sequence A017991 A065614 A058356
Adjacent sequences: A091711 A091712 A091713 this_sequence A091715 A091716 A091717
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jan 31 2004
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