OFFSET
0,4
COMMENTS
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
MAPLE
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:
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 25 2001
STATUS
approved