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A071943
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Triangle T(n,k) read by rows giving number of underdiagonal lattice paths from (0,0) to (n,k) using only steps R=(1,0), V=(0,1) and D=(1,2).
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3
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1, 1, 1, 1, 2, 3, 1, 3, 7, 9, 1, 4, 12, 24, 31, 1, 5, 18, 46, 89, 113, 1, 6, 25, 76, 183, 342, 431, 1, 7, 33, 115, 323, 741, 1355, 1697, 1, 8, 42, 164, 520, 1376, 3054, 5492, 6847, 1, 9, 52, 224, 786, 2326, 5900, 12768, 22669, 28161, 1, 10, 63, 296, 1134, 3684, 10370
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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LINKS
| 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
| G.f.=(1-q)/[z(2t+2t^2z-1+q)], where q=sqrt(1-4tz-4t^2z^2).
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EXAMPLE
| a(3,2)=7 because we have RRRVV, RRVRV, RRVVR, RVRRV, RVRVR, RRD and RDR.
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CROSSREFS
| Diagonal entries yield A052709. Row sums are A071356.
Related arrays: A071944, A071945, A071946.
Sequence in context: A063967 A059397 A152821 * A062869 A102473 A011117
Adjacent sequences: A071940 A071941 A071942 * A071944 A071945 A071946
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KEYWORD
| nonn,easy,tabl
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jun 15 2002
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EXTENSIONS
| Edited by Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 21 2003
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