A005544 -id:A005544 - cp's OEIS frontend

A003287 Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (0,1,1).

1, 4, 22, 140, 970, 7196, 56092, 452064, 3735700, 31484244, 269613896, 2339571468, 20529434520, 181871459580, 1624587752400, 14617165101216

Offset: 1

N. J. A. Sloane

Cf. A001337.

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

D. S. McKenzie, The end-to-end length distribution of self-avoiding walks, J. Phys. A 6 (1973), 338-352.
Index entries for sequences related to f.c.c. lattice

Equals A001337(n+1) / 12 for n > 1.
Equals (n+1) * A005398(n+1) / 6 for n > 1.
Cf. A003288, A005543, A005544, A005545, A005546, A005547, A005548.

A001337 = Cases[Import["https://oeis.org/A001337/b001337.txt", "Table"], {, }][[All, 2]];
a[n_] := If[n == 1, 1, A001337[[n + 1]]/12];
a /@ Range[16] (* Jean-François Alcover, Jan 20 2020 *)

One more term and title improved by Sean A. Irvine, Feb 15 2016

a(15)-a(16) from Bert Dobbelaere, Jan 14 2019

A003288 Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (0,0,2).

Original entry on oeis.org

4, 24, 152, 1080, 8152, 63976, 518232, 4299728, 36360872, 312284536, 2716694880, 23891215320, 212064567160, 1897551819416

Offset: 2

N. J. A. Sloane

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

D. S. McKenzie, The end-to-end length distribution of self-avoiding walks, J. Phys. A 6 (1973), 338-352.
Index entries for sequences related to f.c.c. lattice

Cf. A003287, A005543, A005544, A005545, A005546, A005547, A005548.

More terms and title improved by Sean A. Irvine, Feb 15 2016

a(15) from Bert Dobbelaere, Jan 14 2019

A005543 Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (0,2,2).

Original entry on oeis.org

1, 12, 114, 940, 7568, 61728, 512996, 4334884, 37164700, 322624804, 2830973320, 25074130996, 223900666504, 2013718244072

Offset: 2

N. J. A. Sloane

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

D. S. McKenzie, The end-to-end length distribution of self-avoiding walks, J. Phys. A 6 (1973), 338-352.
Index entries for sequences related to f.c.c. lattice

Cf. A003287, A003288, A005544, A005545, A005546, A005547, A005548.

More terms and title improved by Sean A. Irvine, Feb 15 2016

a(15) from Bert Dobbelaere, Jan 14 2019

A005545 Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (0,1,3).

Original entry on oeis.org

9, 96, 835, 7020, 58857, 497360, 4251804, 36765592, 321262541, 2833702404, 25204186455, 225846648440

Offset: 3

N. J. A. Sloane

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

D. S. McKenzie, The end-to-end length distribution of self-avoiding walks, J. Phys. A 6 (1973), 338-352.
Index entries for sequences related to f.c.c. lattice

Cf. A003287, A003288, A005543, A005544, A005546, A005547, A005548.

More terms and title improved by Sean A. Irvine, Feb 17 2016

A005546 Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (0,3,3).

Original entry on oeis.org

1, 24, 360, 4000, 39330, 367912, 3370604, 30630980, 277824572, 2522478772, 22959239730, 209629138108, 1920548559328

Offset: 3

N. J. A. Sloane

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

D. S. McKenzie, The end-to-end length distribution of self-avoiding walks, J. Phys. A 6 (1973), 338-352.
Index entries for sequences related to f.c.c. lattice

Cf. A003287, A003288, A005543, A005544, A005545, A005547, A005548.

More terms and improved title by Sean A. Irvine, Feb 16 2016

a(15) from Bert Dobbelaere, Jan 14 2019

A005547 Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (1,2,3).

Original entry on oeis.org

3, 52, 575, 5470, 49303, 436446, 3850752, 34063392, 302790797, 2706629188, 24332099665, 219940720414

Offset: 3

N. J. A. Sloane

McKenzie's paper incorrectly gives a(11) = 303790797. - Sean A. Irvine, Feb 17 2016

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

D. S. McKenzie, The end-to-end length distribution of self-avoiding walks, J. Phys. A 6 (1973), 338-352.
Index entries for sequences related to f.c.c. lattice

Cf. A003287, A003288, A005543, A005544, A005545, A005546, A005548.

a(11) corrected, more terms, and title improved by Sean A. Irvine, Feb 17 2016

A005548 Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (2,2,2).

Original entry on oeis.org

6, 72, 690, 6192, 53946, 466800, 4053816, 35450940, 312411672, 2773863060, 24802293720, 223203954264, 2020552369164

Offset: 3

N. J. A. Sloane

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

D. S. McKenzie, The end-to-end length distribution of self-avoiding walks, J. Phys. A 6 (1973), 338-352.
Index entries for sequences related to f.c.c. lattice

Cf. A003287, A003288, A005543, A005544, A005545, A005546, A005547.

More terms and title improved by Sean A. Irvine, Feb 17 2016

a(15) from Bert Dobbelaere, Jan 14 2019

cp's OEIS Frontend

A003287 Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (0,1,1).

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A003288 Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (0,0,2).

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A005543 Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (0,2,2).

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A005545 Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (0,1,3).

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A005546 Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (0,3,3).

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A005547 Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (1,2,3).

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Crossrefs

Extensions

A005548 Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (2,2,2).

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