A059032 - OEIS

%I #4 Mar 30 2012 16:48:58

%S 1,1,3,13,71,487,3965,37306,398048,4748201,62627000,905067008,

%T 14223441093,241516427253,4406723053134,85987611417777,

%U 1786851267779817,39397336701986187,918633226468153628,22585761594590716490,583972625166308889970

%N Another variant of Boustrophedon transform applied to 1, 0, 0, 0, ...

%C 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.

%e Triangle begins

%e ........1

%e ......0...1

%e ....3...2...0

%e ..0...7...11.13

%e 71..67..53..28..0

%e where (say) 53 = 28 + (7+11+3+2+0+0+1+1)

%p 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

%p 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

%Y Cf. A059033, A059034, A059035.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Feb 12 2001