A001394 Number of n-step self-avoiding walks on diamond. (Formerly M3452 N1403)

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

0,2

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

Table of n, a(n) for n=0..27.

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.

Sequence in context: A326339 A334877 A003119 * A156946 A163877 A336262

Adjacent sequences: A001391 A001392 A001393 * A001395 A001396 A001397

Keyword

nonn,walk,nice

Author

N. J. A. Sloane

Extensions

Edited and extended by Joseph Myers, Jul 21 2013

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

Status

approved