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 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). 20
 1, 1, 2, 5, 15, 55, 239, 1199, 6810, 43108, 300731, 2291162, 18923688, 168402163, 1606199354, 16345042652, 176758631046, 2024225038882, 24471719797265, 311446235344127, 4162172487402027, 58275220793611957, 853045299274146032 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..120 EXAMPLE The array begins 1 1 0 5 0 55 0 ... 0 1 3 5 48 55 ... 2 2 8 39 103 ... 0 12 27 152 ... 15 15 190 ... 0 221 ... MAPLE 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) MATHEMATICA 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 *) CROSSREFS Cf. A000667, A059216, A059217, A059220, A059237, A059720, A059718. Sequence in context: A009383 A104429 A109319 * A242275 A137533 A121392 Adjacent sequences:  A059216 A059217 A059218 * A059220 A059221 A059222 KEYWORD easy,nonn,nice AUTHOR N. J. A. Sloane, Jan 18 2001 EXTENSIONS More terms from Floor van Lamoen, Jan 19 2001; and from N. J. A. Sloane Jan 20 2001. STATUS approved

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Last modified August 8 05:25 EDT 2020. Contains 336290 sequences. (Running on oeis4.)