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A091714 Row sums of triangle A052313, which is the matrix square of the triangle of circular binomial coefficients (A047996). 0
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; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=0..29.

FORMULA

a(n) = sum_{k=0..n} A047996(n, k)*A000031(k).

PROG

(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)))

CROSSREFS

Cf. A052313, A047996, A000031.

Sequence in context: A080014 A132274 A253768 * A017991 A065614 A183324

Adjacent sequences:  A091711 A091712 A091713 * A091715 A091716 A091717

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 31 2004

STATUS

approved

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Last modified May 26 17:16 EDT 2020. Contains 334630 sequences. (Running on oeis4.)