A091714 - OEIS

%I #12 Sep 09 2024 15:00:21

%S 1,3,6,10,19,31,68,120,271,567,1302,2918,7199,17071,43110,108642,

%T 280935,727959,1930344,5115348,13765415,37132859,101046712,275870592,

%U 758236999,2088996227,5783712268,16055661688,44729027703,124907034471

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

%C 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.

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

%o (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))))}

%o a(n)=sum(k=0,n, A047996(n,k)*sum(j=0,k, A047996(k,j)))

%Y Cf. A052313, A047996, A000031.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jan 31 2004