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.
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
Offset: 5
Keywords
Links
- 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
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