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A247298 Number of weighted lattice paths B(n) having no uudd strings. 1
1, 1, 2, 4, 8, 17, 36, 80, 180, 410, 946, 2203, 5173, 12233, 29108, 69643, 167437, 404311, 980125, 2384441, 5819576, 14245384, 34964611, 86032272, 212172668, 524371704, 1298509438, 3221425567, 8005623916, 19926840746, 49674610998, 124006308008 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
B(n) is the set of lattice paths of weight n that start in (0,0), end on the horizontal axis and never go below this axis, whose steps are of the following four kinds: h = (1,0) of weight 1, H = (1,0) of weight 2, u = (1,1) of weight 2, and d = (1,-1) of weight 1. The weight of a path is the sum of the weights of its steps.
a(n) = A247297(n,0).
LINKS
M. Bona and A. Knopfmacher, On the probability that certain compositions have the same number of parts, Ann. Comb., 14 (2010), 291-306.
FORMULA
G.f. G = G(z) satisfies G = 1 + z*G + z^2*G + z^3*G*(G - z^3 ).
EXAMPLE
a(6)=36 because among the 37 (=A004148(7)) paths in B(6) only uudd contains uudd.
MAPLE
eq := G = 1+z*G+z^2*G+z^3*G*(G-z^3): G := RootOf(eq, G): Gser := series(G, z = 0, 37): seq(coeff(Gser, z, n), n = 0 .. 35);
CROSSREFS
Sequence in context: A202844 A093951 A137255 * A325928 A076892 A106462
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Sep 17 2014
STATUS
approved

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Last modified March 3 04:18 EST 2024. Contains 370499 sequences. (Running on oeis4.)