cp's OEIS Frontend

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

%I A059032 #4 Mar 30 2012 16:48:58
%S A059032 1,1,3,13,71,487,3965,37306,398048,4748201,62627000,905067008,
%T A059032 14223441093,241516427253,4406723053134,85987611417777,
%U A059032 1786851267779817,39397336701986187,918633226468153628,22585761594590716490,583972625166308889970
%N A059032 Another variant of Boustrophedon transform applied to 1, 0, 0, 0, ...
%C A059032 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 A059032 Triangle begins
%e A059032 ........1
%e A059032 ......0...1
%e A059032 ....3...2...0
%e A059032 ..0...7...11.13
%e A059032 71..67..53..28..0
%e A059032 where (say) 53 = 28 + (7+11+3+2+0+0+1+1)
%p A059032 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 A059032 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 A059032 Cf. A059033, A059034, A059035.
%K A059032 nonn
%O A059032 0,3
%A A059032 _N. J. A. Sloane_, Feb 12 2001