This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A059219 #16 Mar 02 2015 16:08:45
%S A059219 1,1,2,5,15,55,239,1199,6810,43108,300731,2291162,18923688,168402163,
%T A059219 1606199354,16345042652,176758631046,2024225038882,24471719797265,
%U A059219 311446235344127,4162172487402027,58275220793611957,853045299274146032
%N A059219 Variation of Boustrophedon transform applied to sequence 1,0,0,0,...: fill an array by diagonals in alternating directions - 'up' and 'down'. The first element of each diagonal after the first is 0. When 'going up', add to the previous element the elements of the row the new element is in. When 'going down', add to the previous element the elements of the column the new element is in. The final element of the n-th diagonal is a(n).
%H A059219 Vincenzo Librandi, <a href="/A059219/b059219.txt">Table of n, a(n) for n = 0..120</a>
%H A059219 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%e A059219 The array begins
%e A059219 1 1 0 5 0 55 0 ...
%e A059219 0 1 3 5 48 55 ...
%e A059219 2 2 8 39 103 ...
%e A059219 0 12 27 152 ...
%e A059219 15 15 190 ...
%e A059219 0 221 ...
%p A059219 aaa := proc(m,n) option remember; local j,s,t1; if m=0 and n=0 then RETURN(1); fi; if n = 0 and m mod 2 = 1 then RETURN(0); fi; if m = 0 and n mod 2 = 0 then RETURN(0); fi; s := m+n; if s mod 2 = 1 then t1 := aaa(m+1,n-1); for j from 0 to n-1 do t1 := t1+aaa(m,j); od: else t1 := aaa(m-1,n+1); for j from 0 to m-1 do t1 := t1+aaa(j,n); od: fi; RETURN(t1); end; # the n-th antidiagonal in the up direction is aaa(n,0), aaa(n-1,1), aaa(n-2,2), ..., aaa(0,n)
%t A059219 max = 22; t[0, 0] = 1; t[0, _?EvenQ] = 0; t[_?OddQ, 0] = 0; t[n_, k_] /; OddQ[n+k](* up *):= t[n, k] = t[n+1, k-1] + Sum[t[n, j], {j, 0, k-1}]; t[n_, k_] /; EvenQ[n+k](* down *):= t[n, k] = t[n-1, k+1] + Sum[t[j, k], {j, 0, n-1}]; tnk = Table[t[n, k], {n, 0, max}, {k, 0, max-n}]; Join[{1}, Rest[Union[tnk[[1]], tnk[[All, 1]]]]](* _Jean-François Alcover_, May 16 2012 *)
%Y A059219 Cf. A000667, A059216, A059217, A059220, A059237, A059720, A059718.
%K A059219 easy,nonn,nice
%O A059219 0,3
%A A059219 _N. J. A. Sloane_, Jan 18 2001
%E A059219 More terms from _Floor van Lamoen_, Jan 19 2001; and from _N. J. A. Sloane_ Jan 20 2001.