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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

Table of n, a(n) for n=0..31.

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

Cf. A004148, A247297.

Sequence in context: A202844 A093951 A137255 * A325928 A076892 A106462

Adjacent sequences:  A247295 A247296 A247297 * A247299 A247300 A247301

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Sep 17 2014

STATUS

approved

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Last modified September 18 20:13 EDT 2019. Contains 327181 sequences. (Running on oeis4.)