%I #5 Jun 14 2017 00:30:10
%S 1,1,1,2,3,3,5,8,11,11,16,24,35,46,46,62,86,121,167,213,213,275,361,
%T 482,649,862,1075,1075,1350,1711,2193,2842,3704,4779,5854,5854,7204,
%U 8915,11108,13950,17654,22433,28287,34141,34141,41345,50260,61368,75318
%N Triangle, read by rows, defined by T(n,k) = T(n-1,k) + T(n,k-1) for nk>0, where T(n,0) = T(n-1,0) + T(n-1,n-1) and T(n,n) = T(n,n-1) for n>0 with T(0,0)=1.
%e Triangle begins:
%e 1;
%e 1, 1;
%e 2, 3, 3;
%e 5, 8, 11, 11;
%e 16, 24, 35, 46, 46;
%e 62, 86, 121, 167, 213, 213;
%e 275, 361, 482, 649, 862, 1075, 1075;
%e 1350, 1711, 2193, 2842, 3704, 4779, 5854, 5854;
%e 7204, 8915, 11108, 13950, 17654, 22433, 28287, 34141, 34141; ...
%o (PARI) T(n,k)=if(n<k || k<0,0,if(n<=1,1,if(n==k,T(n,k-1),if(k==0,T(n-1,0)+T(n-1,n-1), T(n-1,k)+T(n,k-1)))))
%Y Cf. A129578 (column 0), A129579 (main diagonal), A129580 (row sums).
%K nonn,tabl
%O 0,4
%A _Paul D. Hanna_, Apr 24 2007