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

Author

N. J. A. Sloane, Feb 12 2001

Keywords

• nonn

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.

Examples

			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)
		

Crossrefs

Cf. A059033, A059034, A059035.

Programs

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