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Search: id:A071944
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| A071944 |
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Triangle read by rows giving numbers of paths in a lattice satisfying certain conditions. |
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+0
3
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| 1, 1, 1, 1, 2, 2, 1, 3, 5, 6, 1, 4, 9, 16, 19, 1, 5, 14, 31, 54, 63, 1, 6, 20, 52, 111, 188, 219, 1, 7, 27, 80, 197, 405, 676, 787, 1, 8, 35, 116, 320, 752, 1508, 2492, 2897, 1, 9, 44, 161, 489, 1276, 2900, 5712, 9361, 10869, 1, 10, 54, 216, 714, 2034, 5095, 11296, 21933
(list; table; graph; listen)
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OFFSET
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0,5
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REFERENCES
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D. Merlini, D. G. Rogers, R. Sprugnoli and M. C. Verri, On some alternative characterizations of Riordan arrays, Canad J. Math., 49 (1997), 301-320.
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LINKS
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D. Merlini, D. G. Rogers, R. Sprugnoli and M. C. Verri, On some alternative characterizations of Riordan arrays, Canad J. Math., 49 (1997), 301-320.
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FORMULA
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a(n, k)=[(n-k+1)/(n+1)]sum(binomial(n+1, i)binomial(n+k-3i, n), i=0..k/3) for k<=n.
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MAPLE
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a := proc(n, k) if k<=n then (n-k+1)*sum(binomial(n+1, i)*binomial(n+k-3*i, n), i=0..k/3)/(n+1) else 0 fi end;
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CROSSREFS
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Diagonal entries form A071969.
Adjacent sequences: A071941 A071942 A071943 this_sequence A071945 A071946 A071947
Sequence in context: A059718 A076038 A095788 this_sequence A080955 A125231 A117919
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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njas, Jun 15 2002
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 19 2003
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