A180898 Number of sequences of n integers p(i), i=0..n-1, with 0 <= p(i) <= 2*i and |p(i) - p(i-1)| <= 2.

1, 3, 12, 51, 226, 1025, 4724, 22022, 103550, 490191, 2333057, 11153428, 53517672, 257600811, 1243270807, 6014482911, 29155412470, 141587439283, 688697290541, 3354726880350, 16362475911945, 79900712888835, 390585409850935

Offset

1,2

Comments

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

Column 2 of A180906.

Alternatively, this sequence corresponds to the number of nonnegative walks with n-1 steps {-2,-1,0,1,2} 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

Cf. A180906.

Sequence in context: A151182 A151316 A151183 * A110167 A151317 A151184

Adjacent sequences: A180895 A180896 A180897 * A180899 A180900 A180901

Keyword

nonn

Author

R. H. Hardin, Sep 23 2010

Status

approved