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A261897
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Triangle read by rows: T(n,k) (1 <= k <= n+1) = number of sequences of length n, dominated by the squares, with entries from [0,k] and largest entry k.
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3
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1, 1, 1, 0, 2, 1, 0, 2, 3, 1, 0, 2, 5, 4, 1, 0, 0, 7, 9, 5, 1, 0, 0, 7, 16, 14, 6, 1, 0, 0, 7, 23, 30, 20, 7, 1, 0, 0, 7, 30, 53, 50, 27, 8, 1, 0, 0, 7, 37, 83, 103, 77, 35, 9, 1, 0, 0, 0, 44, 120, 186, 180, 112, 44, 10, 1, 0, 0, 0, 44, 164, 306, 366, 292, 156, 54, 11, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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COMMENTS
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LINKS
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EXAMPLE
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Triangle begins:
1,
1,1,
0,2,1,
0,2,3,1,
0,2,5,4,1,
0,0,7,9,5,1,
0,0,7,16,14,6,1,
0,0,7,23,30,20,7,1,
0,0,7,30,53,50,27,8,1,
0,0,7,37,83,103,77,35,9,1,
0,0,0,44,120,186,180,112,44,10,1,
0,0,0,44,164,306,366,292,156,54,11,1,
...
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PROG
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(Haskell)
a261897 n k = a261897_tabl !! n !! (k-1)
a261897_row n = a261897_tabl !! n
a261897_tabl = [1] : f 1 0 [1] where
f t h xs | t <= (h + 1) ^ 2 = ys : f (t + 1) h ys
| otherwise = ys' : f (t + 1) (h + 1) ys'
where ys = zipWith (+) ([0] ++ xs) (xs ++ [0])
ys' = zipWith (+) ([0] ++ xs) (us ++ (0:vs) ++ [0])
(us, _:vs) = splitAt h xs
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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