A059032 Another variant of Boustrophedon transform applied to 1, 0, 0, 0, ...

1, 1, 3, 13, 71, 487, 3965, 37306, 398048, 4748201, 62627000, 905067008, 14223441093, 241516427253, 4406723053134, 85987611417777, 1786851267779817, 39397336701986187, 918633226468153628, 22585761594590716490, 583972625166308889970

Offset

0,3

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.

Links

Table of n, a(n) for n=0..20.

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)

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

Crossrefs

Cf. A059033, A059034, A059035.

Sequence in context: A137983 A327677 A307005 * A214812 A188051 A247230

Adjacent sequences: A059029 A059030 A059031 * A059033 A059034 A059035

Keyword

nonn

Author

N. J. A. Sloane, Feb 12 2001

Status

approved