A180900 Number of sequences of n integers p(i) i=0..n-1 with 0 <= p(i) <= 4*i and |p(i) - p(i-1)| <= 4.

1, 5, 35, 265, 2100, 17075, 141246, 1182719, 9994086, 85049639, 727865758, 6257933219, 54010196582, 467657712902, 4060558796894, 35341693437365, 308249001184768, 2693524485431382, 23575195919671458, 206647076624751357

Offset

1,2

Comments

Paths down an n-high rectangular-grid right triangle with interior neighbor fanout 2*4 + 1.

Column 4 of A180906.

Alternatively, this sequence corresponds to the number of nonnegative walks with n steps {-4,-3,-2,-1,0,1,2,3,4} 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: A196661 A104532 A292839 * A344840 A087630 A084135

Adjacent sequences: A180897 A180898 A180899 * A180901 A180902 A180903

Keyword

nonn

Author

R. H. Hardin, Sep 23 2010

Status

approved