A059294 2-boustrophedon transform applied to 1, 0, 0, 0, ...

1, 1, 1, 3, 13, 73, 505, 4143, 39313, 423401, 5101785, 67994611, 993048765, 15770916657, 270586214481, 4987678532991, 98297729816321, 2062591323728689, 45908909743929681, 1080350557160580163, 26800186367114537613, 698982753383076195897

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

Links

Table of n, a(n) for n=0..21.

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

Sequence in context: A367749 A367748 A318617 * A124468 A352302 A205572

Adjacent sequences: A059291 A059292 A059293 * A059295 A059296 A059297

Keyword

nonn

Author

N. J. A. Sloane, Jan 25 2001

Status

approved