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A059032
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Another variant of Boustrophedon transform applied to 1, 0, 0, 0, ...
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6
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1, 1, 3, 13, 71, 487, 3965, 37306, 398048, 4748201, 62627000, 905067008, 14223441093, 241516427253, 4406723053134, 85987611417777, 1786851267779817, 39397336701986187, 918633226468153628, 22585761594590716490, 583972625166308889970
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Read rows of triangle alternately from left to right, then right to left. Initial entries of rows are input sequence b[0], b[1], ...; final entries of rows form output a[1], a[1], ... Entry in row is sum of previous entry in same row plus ALL entries in triangle above the new position.
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EXAMPLE
| Triangle begins
........1
......0...1
....3...2...0
..0...7...11.13
71..67..53..28..0
where (say) 53 = 28 + (7+11+3+2+0+0+1+1)
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MAPLE
| T059032 := proc(i, j) option remember; local r, s, t1; if i=0 and j mod 2 = 0 then RETURN(b[j+1]); fi; if j=0 and i mod 2 = 1 then RETURN(b[i+1]); fi; if i+j mod 2 = 1 then t1 := T059032(i+1, j-1); for r from 0 to i do for s from 0 to j do if r+s <> i+j then t1 := t1+T059032(r, s); fi; od: od: else t1 := T059032(i-1, j+1); for r from 0 to i do for s from 0 to j do if r+s <> i+j then t1 := t1+T059032(r, s); fi; od: od: fi; RETURN(t1); end; # that makes the triangle
b := [1, seq(0, i=1..200)]; A059032 := n->if n mod 2 = 0 then T059032(n, 0) else T059032(0, n); fi; # produces the transform
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CROSSREFS
| Cf. A059033, A059034, A059035.
Sequence in context: A000261 A111140 A137983 * A188051 A047159 A086662
Adjacent sequences: A059029 A059030 A059031 * A059033 A059034 A059035
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Feb 12 2001
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