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

Author

Paul D. Hanna, Jan 31 2004

Keywords

• nonn

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.

Crossrefs

Cf. A052313, A047996, A000031.

Programs

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)))

Formula

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