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A059219
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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).
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19
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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; internal format)
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OFFSET
| 0,3
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LINKS
| Index entries for sequences related to boustrophedon transform
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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 ...
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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)
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CROSSREFS
| Cf. A000667, A059216, A059217, A059220, A059237, A059720, A059718.
Sequence in context: A009383 A104429 A109319 * A137533 A121392 A119611
Adjacent sequences: A059216 A059217 A059218 * A059220 A059221 A059222
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KEYWORD
| easy,nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 18 2001
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EXTENSIONS
| More terms from Floor van Lamoen (fvlamoen(AT)hotmail.com), Jan 19 2001; and from N. J. A. Sloane (njas(AT)research.att.com) Jan 20 2001.
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