A091714 Row sums of triangle A052313, which is the matrix square of the triangle of circular binomial coefficients (A047996).

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

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: A373803 A132274 A253768 * A017991 A065614 A183324

Adjacent sequences: A091711 A091712 A091713 * A091715 A091716 A091717

Keyword

nonn

Author

Paul D. Hanna, Jan 31 2004

Status

approved