A089941 Row sums of triangle A089940.

1, 2, 4, 9, 19, 42, 90, 197, 424, 923, 1989, 4315, 9300, 20129, 43374, 93724, 201888, 435713, 938218, 2022972, 4354569, 9382489, 20190181, 43477688, 93534469, 201326672, 433017364, 931701321, 2003520121, 4309597827, 9265723250

Offset: 0

Author

Paul Barry, Nov 16 2003

Keywords

• easy
• nonn

Formula

a(n)=sum{k=0..n, Bin(n+k, floor((n-k)/2))}.

Conjecture: +n*(n+6)*(n-5)*a(n) -(n+6)*(n^2-3*n-6)*a(n-1) -2*(n+6)*(3*n^2-20*n

+27)*a(n-2) +(n+6)*(3*n^2-19*n+36)*a(n-3) +2*(4*n-15)*(n-3)*(n+6)*a(n-4) +4*(n-3

)*(n-4)*(n+6)*a(n-5)=0. - R. J. Mathar, Dec 10 2014