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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
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Sep 23 2010
STATUS
approved