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A100691 Number of self-avoiding paths with n steps on a triangular lattice in the strip Z x {0,1}. 0
1, 4, 12, 30, 70, 158, 352, 780, 1724, 3806, 8398, 18526, 40864, 90132, 198796, 438462, 967062, 2132926, 4704320, 10375708, 22884348, 50473022, 111321758, 245527870, 541528768, 1194379300, 2634286476, 5810101726, 12814582758 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

J. Labelle, Paths in the Cartesian, triangular and hexagonal lattices, Bulletin of the ICA, 17, 1996, 47-61.

LINKS

Table of n, a(n) for n=0..28.

FORMULA

G.f.: (1+z^2)(1+z+z^2)/[(1-z)(1-2z-z^3)].

a(n) = 2*a(n-1) + a(n-3) + 6 for n >= 4.

a(n) = A008998(n+2) - A052980(n+1) - 3. - Ralf Stephan, May 15 2007

MAPLE

g:=series((1+z^2)*(1+z+z^2)/(1-z)/(1-2*z-z^3), z=0, 35): 1, seq(coeff(g, z^n), n=1..34);

CROSSREFS

Sequence in context: A037166 A118892 A036388 * A000298 A218009 A249914

Adjacent sequences:  A100688 A100689 A100690 * A100692 A100693 A100694

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Dec 07 2004

STATUS

approved

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Last modified March 8 11:48 EST 2021. Contains 341948 sequences. (Running on oeis4.)