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Search: id:A107842
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| A107842 |
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A number triangle of lattice walks. |
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+0
2
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| 1, 2, 1, 5, 5, 1, 14, 20, 8, 1, 42, 75, 44, 11, 1, 132, 275, 208, 77, 14, 1, 429, 1001, 910, 440, 119, 17, 1, 1430, 3640, 3808, 2244, 798, 170, 20, 1, 4862, 13260, 15504, 10659, 4655, 1309, 230, 23, 1, 16796, 48450, 62016, 48279, 24794, 8602, 2000, 299, 26, 1
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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First column is A000108(n+1). Columns include A000344, A003518 and A000589. Row sums are A026671. Compare [1,1,1,...] DELTA [0,1,0,0,...] where DELTA is the operator defined in A084938.
Transposed version in A109450 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 05 2007
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FORMULA
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Number triangle T(n, k)=(3k+2)*C(2n+k+1, n-k)/(n+2k+2); Column k has g.f. x^k*C(x)^(3k+2) where C(x) is the g.f. of A000108.
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EXAMPLE
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Triangle begins
1;
2,1;
5,5,1;
14,20,8,1;
42,75,44,11,1;
Triangle [1,1,1,1,1,...] DELTA [0,1,0,0,0,0,...] begins:
1;
1, 0;
2, 1, 0;
5, 5, 1, 0;
14, 20, 8, 1, 0;
42, 75, 44, 11, 1, 0;
132, 275, 208, 77, 14, 1, 0 ; ...
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CROSSREFS
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Sequence in context: A079502 A126124 A060920 this_sequence A126216 A124733 A137597
Adjacent sequences: A107839 A107840 A107841 this_sequence A107843 A107844 A107845
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 24 2005
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