A180899 Number of sequences of n integers p(i) i=0..n-1 with 0 <= p(i) <= 3*i and |p(i) - p(i-1)| <= 3.

1, 4, 22, 130, 803, 5085, 32747, 213419, 1403399, 9292850, 61877337, 413894378, 2779029389, 18719276722, 126438191373, 856054836170, 5808041074705, 39478084788582, 268776967284806, 1832579782914892, 12511376749656415

Offset

1,2

Comments

Paths down an n-high rectangular-grid right triangle with interior neighbor fanout 2*3 + 1.

Column 3 of A180906.

Alternatively, this sequence corresponds to the number of nonnegative walks with n steps {-3,-2,-1,0,1,2,3} starting at the origin, ending at any altitude, and not going below the x-axis. - David Nguyen, Dec 01 2016

Links

R. H. Hardin, Table of n, a(n) for n=1..100

C. Banderier, C. Krattenthaler, A. Krinik, D. Kruchinin, V. Kruchinin, D. Nguyen, and M. Wallner, Explicit formulas for enumeration of lattice paths: basketball and the kernel method, arXiv:1609.06473 [math.CO], 2016.

Crossrefs

Sequence in context: A155862 A088536 A066380 * A007195 A356283 A292838

Adjacent sequences: A180896 A180897 A180898 * A180900 A180901 A180902

Keyword

nonn

Author

R. H. Hardin, Sep 23 2010

Status

approved