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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 (list; graph; refs; listen; history; text; internal format)



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


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).


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.


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




N. J. A. Sloane.


Edited and extended by Joseph Myers, Jul 21 2013

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



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Last modified July 25 09:49 EDT 2021. Contains 346289 sequences. (Running on oeis4.)