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 A128737 Number of LDU's in all skew Dyck paths of semilength n. 1
 0, 0, 0, 0, 1, 10, 69, 412, 2291, 12244, 63886, 328256, 1669363, 8429384, 42349096, 211982828, 1058244079, 5272285552, 26227527576, 130323237088, 647013004499, 3210128312122, 15919166804461, 78915323039268, 391100149306301 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS A skew Dyck path is a path in the first quadrant which begins at the origin, ends on the x-axis, consists of steps U=(1,1)(up), D=(1,-1)(down) and L=(-1,-1)(left) so that up and left steps do not overlap. The length of the path is defined to be the number of its steps. LINKS E. Deutsch, E. Munarini, S. Rinaldi, Skew Dyck paths, J. Stat. Plann. Infer. 140 (8) (2010) 2191-2203 FORMULA a(n) = Sum_{k>=0} k*A128735(n,k). G.f.: z(g-1)^3/(4g - 2zg - 6zg^2 - 3 + 3*z), where g = 1 + zg^2 + z(g-1) = (1 - z - sqrt(1 - 6z + 5z^2))/(2z). Conjecture: -10*(n+1)*(n-4)*a(n) +(73*n^2-273*n+140)*a(n-1) +(-132*n^2+641*n-734) *a(n-2) +(n-3)*(89*n-269)*a(n-3) -20*(n-3)*(n-4)*a(n-4)=0. - R. J. Mathar, Jun 17 2016 EXAMPLE a(4)=1 because among the 36 (=A002212(4)) skew Dyck paths of semilength 4 only UUUDLDUD has a LDU. MAPLE g:=(1-z-sqrt(1-6*z+5*z^2))/2/z: ser:=series(z*(g-1)^3/(4*g-2*z*g-6*z*g^2-3+3*z), z=0, 30): seq(coeff(ser, z, n), n=0..27); CROSSREFS Cf. A128735. Sequence in context: A081280 A038806 A016273 * A320228 A130548 A160662 Adjacent sequences:  A128734 A128735 A128736 * A128738 A128739 A128740 KEYWORD nonn AUTHOR Emeric Deutsch, Mar 31 2007 STATUS approved

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Last modified April 25 12:04 EDT 2019. Contains 322456 sequences. (Running on oeis4.)