0,3

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.

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)

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

Cf. A059033, A059034, A059035.

Sequence in context: A000261 A111140 A137983 this_sequence A047159 A086662 A090754

Adjacent sequences: A059029 A059030 A059031 this_sequence A059033 A059034 A059035

nonn

N. J. A. Sloane (njas(AT)research.att.com), Feb 12 2001