A337907 The number of walks of n steps on the hexagonal lattice that start at the origin and end at the non-adjacent vertex (3/2,sqrt(3)/2).

2, 6, 48, 220, 1320, 6930, 39200, 215208, 1208340, 6754440, 38076192, 214939296, 1218641424, 6925848930, 39477746880, 225542306704, 1291514481972, 7410367503396, 42599109627360, 245305128355560, 1414839151645920, 8172376003368720, 47270088643265280, 273766119948648000

Offset

2,1

Links

Table of n, a(n) for n=2..25.

Formula

D-finite with recurrence -(n-2)*(n+3)*(n+2)*(n+1)*a(n) +n*(n+2)*(n^2+n+12)*a(n-1) +24*n*(n-1)*(n^2+3*n-1)*a(n-2) +36*n*(n-1)*(n-2)*(n+4)*a(n-3)=0.

Example

There are a(2)=2 paths with 2 steps: RU and UR, where R=(1,0), L=(-1,0), U=(1/2,sqrt(3)/2), u=(-1/2,sqrt(3)/2), D=(1/2,-sqrt(3)/2), d=(-1/2,-sqrt(3)/2).
There are a(3)=6 paths with 3 steps: UUD, UDU, DUU, RRu, RuR, uRR.

Maple

# see A337905

Crossrefs

Cf. A002898 (returns to origin), A337905, A337906.

Sequence in context: A052596 A344676 A098710 * A052614 A052688 A052657

Adjacent sequences: A337904 A337905 A337906 * A337908 A337909 A337910

Keyword

nonn,walk

Author

R. J. Mathar, Sep 29 2020

Status

approved