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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

Index entries for sequences related to boustrophedon transform

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-Fran├žois 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.)