A268399 Number of North-East lattice paths from (0,0) to (n,n) that have exactly four east steps below the subdiagonal y = x-1.

14, 70, 286, 1099, 4124, 15327, 56770, 210188, 779076, 2893111, 10767680, 40171225, 150229560, 563151435, 2115877410, 7967261640, 30063189300, 113663662560, 430549220244, 1633782030774, 6210024076424, 23641792007350, 90140083306676, 344168324083080, 1315850249846440, 5037257160310193

Offset

5,1

Comments

This sequence is related to paired pattern P_1 in Pan and Remmel's link.

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) + 2*x)^2*(-1 + f(x) + x*(2*f(x) + x + 5*f(x)*x - 10*x^2)))/(8*x^2), where f(x) = sqrt(1 - 4*x).

Conjecture: -(n+2)*(641*n-5292)*a(n) +(-641*n^2-1681*n+22692)*a(n-1) +(-4067*n^2+10502*n+80184) *a(n-2) +6*(5629*n-11668)*(2*n-11) *a(n-3)=0. - R. J. Mathar, Jun 07 2016

Conjecture: +(n+2)*(1023*n^2-11311*n+23730) *a(n) +(1023*n^3+15038*n^2-85751*n+44490)*a(n-1) -10*(2*n-9) *(1023*n^2-2563*n+1450)*a(n-2)=0. - R. J. Mathar, Jun 07 2016

Crossrefs

Cf. A268370.

Sequence in context: A201106 A337641 A213160 * A034554 A246507 A034562

Adjacent sequences: A268396 A268397 A268398 * A268400 A268401 A268402

Keyword

nonn

Author

Ran Pan, Feb 03 2016

Status

approved