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A071945 Triangle T(n,k) read by rows giving number of underdiagonal lattice paths from (0,0) to (n,k) using steps R=(1,0), V=(0,1) and D=(2,1). 5
1, 1, 1, 1, 3, 3, 1, 5, 9, 9, 1, 7, 19, 31, 31, 1, 9, 33, 73, 113, 113, 1, 11, 51, 143, 287, 431, 431, 1, 13, 73, 249, 609, 1153, 1697, 1697, 1, 15, 99, 399, 1151, 2591, 4719, 6847, 6847, 1, 17, 129, 601, 2001, 5201, 11073, 19617, 28161, 28161, 1, 19, 163, 863, 3263 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..59.

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.

FORMULA

G.f.=(1-q)/[z(1+tz)(2t-1+q)], where q=sqrt(1-4tz-4t^2z^2).

EXAMPLE

a(3,1)=5 because we have RRRV, RRVR, RVRR, RD and DR

CROSSREFS

Diagonal entries give A052709.

Sequence in context: A248810 A208610 A193823 * A209583 A144944 A137426

Adjacent sequences:  A071942 A071943 A071944 * A071946 A071947 A071948

KEYWORD

nonn,easy,tabl

AUTHOR

N. J. A. Sloane, Jun 15 2002

EXTENSIONS

Edited by Emeric Deutsch, Dec 21 2003

STATUS

approved

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Last modified January 22 12:13 EST 2019. Contains 319363 sequences. (Running on oeis4.)