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%I #4 Mar 30 2012 18:51:35
%S 1,1,1,1,2,3,1,3,5,9,1,4,8,14,27,1,5,12,22,41,81,1,6,17,34,63,122,243,
%T 1,7,23,51,97,185,365,729,1,8,30,74,148,282,550,1094,2187,1,9,38,104,
%U 222,430,832,1644,3281,6561,1,10,47,142,326,652,1262,2476,4925,9842
%N Triangle where T(n,k)=2*T(n,k-1)+C(n-1,k)-C(n-1,k-1) and n>=k>=0.
%F T(n, k)=2*T(n, k-1)+A037012(n, k). T(n, k)=T(n-1, k-1)+T(n-1, k) if k<n. T(n, n)=Sum_{j<n}T(n, j)=3^(n-1) if n>0.
%e Rows start 1; 1,1; 1,2,3; 1,3,5,9; 1,4,8,14,27; etc. T(4,0)=2*0+1-0=1; T(4,1)=2*1+3-1=4; T(4,2)=2*4+3-3=8; T(4,3)=2*8+1-3=14; T(4,4)=2*14+0-1=27.
%Y Row sums are A025192. Columns include A000012, A000027 and A022856 (essentially). Right hand columns include A000244 (essentially), A007051 and A047926. Central diagonal is A067336.
%K nonn,tabl
%O 0,5
%A _Henry Bottomley_, Jan 15 2002
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