A001394 Number of n-step self-avoiding walks on diamond.

1, 4, 12, 36, 108, 324, 948, 2796, 8196, 24060, 70188, 205284, 597996, 1744548, 5073900, 14774652, 42922452, 124814484, 362267652, 1052271732, 3051900516, 8857050204, 25671988020, 74449697484, 215677847460, 625096195404, 1810062340812, 5243388472212

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• walk
• nice

Comments

Number of 2 X n binary matrices avoiding simultaneously the right-angled numbered polyomino patterns (ranpp) (00;1) and (01;1). An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1 < i2, j1 < j2 and these elements are in same relative order as those in the triple (x,y,z). - Sergey Kitaev, Nov 11 2004

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• J. W. Essam and M. F. Sykes, The crystal statistics of the diamond lattice, Physica, 29 (1963), 378-388.
• A. J. Guttmann, On the critical behavior of self-avoiding walks II, J. Phys. A 22 (1989), 2807-2813.
• S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.
• S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, University of Kentucky Research Reports (2004).
• J. L. Martin, The exact enumeration of self-avoiding walks on a lattice, Proc. Camb. Phil. Soc., 58 (1962), 92-101.

Crossrefs

Cf. A001395, A001396, A001397, A001398, A097700, A176086, A227715, A227716.

Extensions

Edited and extended by Joseph Myers, Jul 21 2013

a(24)-a(27) from Sean A. Irvine, Nov 13 2017