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%I #14 Mar 14 2015 00:32:08
%S 1,1,1,3,13,73,505,4143,39313,423401,5101785,67994611,993048765,
%T 15770916657,270586214481,4987678532991,98297729816321,
%U 2062591323728689,45908909743929681,1080350557160580163,26800186367114537613,698982753383076195897
%N 2-boustrophedon transform applied to 1, 0, 0, 0, ...
%C The transform takes the original sequence s(0), s(1), s(2),.. and fills the 0th column of a lower triangular array with t(r,0) = s(r). The remaining columns of the triangular array are filled by a sum over the left neighbor plus two entries of the previous row: t(r,c) = t(r,c-1) +t(r-1,r-c) +t(r-1,r-c-1), 1<=c<=r. [The last term in this sum does not exist if r=c and is implicitly defined as t(r-1,-1)=0 then.] The result of the transform is the sequence of numbers t(r,r) along the diagonal of the triangular array for r>=0. - _R. J. Mathar_, Nov 12 2011
%p TBOUS := proc(a) local c,i,j,n: if whattype(a) <> list then RETURN([]); fi: n := min( nops(a), 60); for i from 0 to n-1 do c[i,0] := a[i+1]; od; for i from 1 to n-1 do for j from 1 to i-1 do c[i,j] := c[i,j-1] + c[i-1,i-j] + c[i-1,i-j-1]; od; c[i,i] := c[i,i-1] + c[i-1,0]; od; RETURN([seq(c[i,i],i=0..n-1)]); end:
%K nonn
%O 0,4
%A _N. J. A. Sloane_, Jan 25 2001