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A337906 The number of walks of n steps on the hexagonal lattice that start at the origin and end at the non-adjacent vertex (2,0). 2
1, 6, 34, 200, 1095, 6230, 34636, 195552, 1099140, 6218520, 35210736, 200099328, 1139401263, 6504768270, 37211008120, 213311576192, 1225053737622, 7047867363108, 40612374024300, 234376628718960, 1354498970905080, 7838134441085520, 45412879702456800, 263417461793120000 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,2
LINKS
FORMULA
D-finite with recurrence (n-2)*(3*n^2-5*n-20)*(n+2)^2*a(n) -n*(3*n^4-2*n^3+n^2-130*n-208)*a(n-1) -24*n*(n-1)*(n-3)*(3*n^2+7*n-2)*a(n-2) -36*n*(n-1)*(n-2)*(3*n^2+n-22)*a(n-3)=0.
EXAMPLE
There is a(2)=1 path with 2 steps: RR, 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: RUD, RDU, DRU, DUR, URD, UDR.
MAPLE
# see A337905
CROSSREFS
Cf. A002898 (returns to origin), A337905, A337907.
Sequence in context: A126501 A218990 A087413 * A244829 A059228 A079568
KEYWORD
nonn,walk
AUTHOR
R. J. Mathar, Sep 29 2020
STATUS
approved

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Last modified June 1 11:52 EDT 2023. Contains 363068 sequences. (Running on oeis4.)