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Search: id:A071947
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| A071947 |
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Triangle read by rows of numbers of paths in a lattice satisfying certain conditions. |
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3
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| 1, 1, 0, 1, 1, 1, 1, 2, 3, 1, 1, 3, 6, 6, 3, 1, 4, 10, 15, 15, 6, 1, 5, 15, 29, 40, 36, 15, 1, 6, 21, 49, 84, 105, 91, 36, 1, 7, 28, 76, 154, 238, 280, 232, 91, 1, 8, 36, 111, 258, 468, 672, 750, 603, 232, 1, 9, 45, 155, 405, 837, 1398, 1890, 2025, 1585, 603, 1, 10, 55, 209, 605
(list; table; graph; listen)
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OFFSET
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0,8
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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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G.f.=t(1+tz-q)/[(1+tz)(2t^2*z+tz-1+q)], where q=sqrt(1-2tz-3t^2*z^2).
Sum_{k, 0<=k<=n}T(n,k)*2^(n-k) = A112657(n). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 01 2007
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EXAMPLE
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1; 1,0; 1,1,1; 1,2,3,1; 1,3,6,6,3; 1,4,10,15,15,6;
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CROSSREFS
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Row sums give A002426 (central trinomial coefficients). Reversal of A089942.
Sequence in context: A004648 A139438 A135392 this_sequence A139343 A059247 A023570
Adjacent sequences: A071944 A071945 A071946 this_sequence A071948 A071949 A071950
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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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Edited by Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 04 2004
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