A000760 -id:A000760 - cp's OEIS frontend

A227338 Number of n-step self-avoiding walks on cubic lattice ending at point with x = k.

1, 4, 1, 12, 8, 1, 44, 40, 12, 1, 172, 176, 84, 16, 1, 772, 748, 468, 144, 20, 1, 3308, 3248, 2332, 984, 220, 24, 1, 14924, 14280, 11068, 5756, 1788, 312, 28, 1, 64956, 63768, 51472, 30760, 12108, 2944, 420, 32, 1, 294252, 285296, 237832, 155912, 72948, 22732, 4516

Offset: 0

Joseph Myers, Jul 07 2013

The number of walks ending with x = -k is the same as the number ending with x = k.

			Initial rows (paths of length 0, 1, 2, ...):
1;
4, 1;
12, 8, 1;
44, 40, 12, 1;
...

Bert Dobbelaere, Table of n, a(n) for n = 0..275 (terms 0..152 from Joseph Myers)
J. L. Martin, The exact enumeration of self-avoiding walks on a lattice, Proc. Camb. Phil. Soc., 58 (1962), 92-101.

Cf. A000759, A000760, A000761, A000762, A001412.

For n > 0, A001412(n) = T(n,0) + 2 * Sum_{k=1..n} T(n,k). - Bert Dobbelaere, Jan 06 2019

A000759 Number of n-step self-avoiding walks on cubic lattice ending at point with x=0.

Original entry on oeis.org

1, 4, 12, 44, 172, 772, 3308, 14924, 64956, 294252, 1301044, 5930588, 26506948, 121290940, 546050988, 2505533940, 11340303508, 52147596788, 236995050900, 1091701675948, 4977541017540, 22961416861940, 104965762062612

Offset: 0

N. J. A. Sloane

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).

J. L. Martin, The exact enumeration of self-avoiding walks on a lattice, Proc. Camb. Phil. Soc., 58 (1962), 92-101.

Cf. A000760, A000761, A000762, A001412, A227338.

Edited and extended by Joseph Myers, Jul 07 2013

a(17)-a(22) from Bert Dobbelaere, Jan 06 2019

A000761 Number of n-step self-avoiding walks on cubic lattice ending at point with x=2.

Original entry on oeis.org

1, 12, 84, 468, 2332, 11068, 51472, 237832, 1095384, 5040568, 23168528, 106496816, 489379904, 2250000884, 10345888480, 47604198576, 219096141188, 1009071461380, 4648802248764, 21431064157200, 98828123716260

Offset: 2

N. J. A. Sloane

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).

J. L. Martin, The exact enumeration of self-avoiding walks on a lattice, Proc. Camb. Phil. Soc., 58 (1962), 92-101.

Cf. A000759, A000760, A000762, A001412, A227338.

Edited and extended by Joseph Myers, Jul 07 2013

a(17)-a(22) from Bert Dobbelaere, Jan 06 2019

A000762 Number of n-step self-avoiding walks on cubic lattice ending at point with x=3.

Original entry on oeis.org

1, 16, 144, 984, 5756, 30760, 155912, 766424, 3698848, 17648312, 83558828, 393534176, 1846227984, 8637479208, 40325165648, 187980582568, 875268197452, 4072021100336, 18931821861960, 87979249474568

Offset: 3

N. J. A. Sloane

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).

J. L. Martin, The exact enumeration of self-avoiding walks on a lattice, Proc. Camb. Phil. Soc., 58 (1962), 92-101.

Cf. A000759, A000760, A000761, A001412, A227338.

Edited and extended by Joseph Myers, Jul 07 2013

a(17)-a(22) from Bert Dobbelaere, Jan 06 2019

cp's OEIS Frontend

A227338 Number of n-step self-avoiding walks on cubic lattice ending at point with x = k.

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A000759 Number of n-step self-avoiding walks on cubic lattice ending at point with x=0.

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A000761 Number of n-step self-avoiding walks on cubic lattice ending at point with x=2.

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A000762 Number of n-step self-avoiding walks on cubic lattice ending at point with x=3.

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