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A126890
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Triangle read by rows: T(n,k) = n*(n+2*k+1)/2, 0 <= k <= n.
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20
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0, 1, 2, 3, 5, 7, 6, 9, 12, 15, 10, 14, 18, 22, 26, 15, 20, 25, 30, 35, 40, 21, 27, 33, 39, 45, 51, 57, 28, 35, 42, 49, 56, 63, 70, 77, 36, 44, 52, 60, 68, 76, 84, 92, 100, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 55, 65, 75, 85, 95, 105, 115, 125, 135, 145, 155, 66, 77, 88
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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REFERENCES
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Léonard Euler, Introduction à l'analyse infinitésimale, tome premier, ACL-Editions, Paris, 1987, p. 353-354.
Adrien-Marie Legendre, Théorie des nombres, tome 2, quatrième partie, p.131, troisième édition, Paris, 1830.
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LINKS
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Émile Fourrey, Les nombres abstraits, Récreations arithmétiques, 1899 and later, Vuibert, Paris, page 86-87. Triangle without right diagonal.
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FORMULA
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EXAMPLE
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Triangle begins:
0;
1, 2;
3, 5, 7;
6, 9, 12, 15;
10, 14, 18, 22, 26;
15, 20, 25, 30, 35, 40;
21, 27, 33, 39, 45, 51, 57;
28, 35, 42, 49, 56, 63, 70, 77; (End)
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MATHEMATICA
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Flatten[Table[(n(n+2k+1))/2, {n, 0, 20}, {k, 0, n}]] (* Harvey P. Dale, Jun 21 2013 *)
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PROG
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(Haskell)
a126890 n k = a126890_tabl !! n !! k
a126890_row n = a126890_tabl !! n
a126890_tabl = map fst $ iterate
(\(xs@(x:_), i) -> (zipWith (+) ((x-i):xs) [2*i+1 ..], i+1)) ([0], 0)
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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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