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A268402 Number of North-East lattice paths from (0,0) to (n,n) that bounce off the diagonal y = x to the right exactly four times. 0
1, 7, 40, 204, 977, 4493, 20091, 88025, 379766, 1618898, 6835636, 28640302, 119236085, 493772409, 2035611612, 8359873866, 34219553297, 139672169795, 568675783762, 2310315996126, 9367885987455, 37920179012135, 153263612914150, 618611076034828, 2493830719572639, 10042451847789161 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,2

COMMENTS

This sequence is related to paired pattern P_2 in Pan and Remmel's link.

By symmetry, it is also the number of North-East lattice paths from (0,0) to (n,n) that bounce off the diagonal y = x to the left exactly four times.

LINKS

Table of n, a(n) for n=5..30.

Ran Pan and Jeffrey B. Remmel, Paired patterns in lattice paths, arXiv:1601.07988 [math.CO], 2016.

FORMULA

G.f.: -((-1 + f(x))^5*x^3*(-1 + f(x) + 2*x))/(2*(1 - f(x) + (-5 + f(x))*x)^5), where f(x) = sqrt(1 - 4*x).

Conjecture: -(n-3)*(n-5)*(55*n-618)*a(n) +(-55*n^3-840*n^2+6969*n-5742)*a(n-1)

  +(3135*n^3 -37532*n^2 +138815*n -163614)*a(n-2) +(-7645*n^3 +93072*n^2 -343985*n +391386)*a(n-3) -18*(n-3)*(55*n-126)*(2*n-5)*a(n-4)=0. - R. J. Mathar, Oct 07 2016

CROSSREFS

Cf. A268400, A268401.

Sequence in context: A055282 A252816 A093737 * A081039 A227748 A083327

Adjacent sequences:  A268399 A268400 A268401 * A268403 A268404 A268405

KEYWORD

nonn

AUTHOR

Ran Pan, Feb 03 2016

STATUS

approved

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Last modified September 26 05:09 EDT 2017. Contains 292502 sequences.