A109000 - OEIS

%I #4 Mar 30 2012 18:36:49

%S 1,1,3,11,37,133,479,1719,6121,21609,75675,263171,909899,3130963,

%T 10730891,36639987,124528283,420319907,1403656123,4615627555,

%U 14868713515,46702912307,142489152555,421113970835,1203581558011

%N Antidiagonal sums of square array A108998, in which row n equals the coordination sequence of B_n lattice.

%C Limit a(n+1)/a(n) ~ 3.3829757679..., real root of cubic (1+x+3*x^2-x^3). Compare to antidiagonal sums A108555 of square array A108553, in which row n equals the crystal ball sequence for D_n lattice.

%F a(n) = Sum_{k=0..n} Sum_{j=0..k} C(n-j-1, k-j) * (C(2*n-2*k+1, 2*j)-2*(n-k)*C(n-k-1, j-1)).

%o (PARI) {a(n)=sum(k=0,n,sum(j=0,k, binomial(n-j-1,k-j)*(binomial(2*n-2*k+1,2*j)-2*(n-k)*binomial(n-k-1,j-1))))}

%Y Cf. A108998, A108999, A109001.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jun 17 2005