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A059294
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2-boustrophedon transform applied to 1, 0, 0, 0, ...
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4
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1, 1, 1, 3, 13, 73, 505, 4143, 39313, 423401, 5101785, 67994611, 993048765, 15770916657, 270586214481, 4987678532991, 98297729816321, 2062591323728689, 45908909743929681, 1080350557160580163, 26800186367114537613, 698982753383076195897
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| The transform takes the original sequence s(0), s(1), s(2),.. and fills the 0-th 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 neighbour 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
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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:
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CROSSREFS
| Sequence in context: A193932 A193933 A000262 * A124468 A205572 A128196
Adjacent sequences: A059291 A059292 A059293 * A059295 A059296 A059297
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 25 2001
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