A334322 -id:A334322 - cp's OEIS frontend

A334326 Number of endless self-avoiding walks of length n on the simple cubic lattice.

6, 30, 126, 606, 2766, 13134, 60990, 286014, 1333926, 6235950, 29160390, 136280046, 637801014, 2981709558, 13958158806, 65278026174, 305608333062, 1429710254742, 6693530115990, 31322452467006, 146644481901582, 686366924272686, 3213444320539710, 15042778398965358

Offset: 1

Michel Marcus, Apr 23 2020

nonn

Nathan Clisby, Endless self-avoiding walks, arXiv:1302.2796 [cond-mat.stat-mech], 2013. See Table 3 column e_n p. 23.

Cf. A334327, A334328, A334329.

Cf. A334322, A334330, A334331, A334332, A334333, A334334.

A334330 Number of endless self-avoiding walks of length 2*n for the honeycomb lattice.

Original entry on oeis.org

1, 6, 18, 60, 210, 726, 2448, 8448, 28818, 98556, 336618, 1150320, 3928944, 13419204, 45828192, 156512220, 534463698, 1825120584, 6232259412, 21281168202, 72666555570, 248124503652, 847224827676, 2892836367066, 9877456541376, 33725891989626

Offset: 0

Michel Marcus, Apr 23 2020

Nathan Clisby, Endless self-avoiding walks, arXiv:1302.2796 [cond-mat.stat-mech], 2013. See Table 4 p. 23.

A001668 counts all self-avoiding walks on the honeycomb lattice, without the "endless" restriction.

Cf. A334322 (square lattice), A334326 (simple cubic lattice), A334331 (triangular lattice), A334332 (union jack lattice), A334333 (body centered cubic lattice), A334334 (face centered cubic lattice).

A334331 Number of endless self-avoiding walks of length n on the triangular lattice.

Original entry on oeis.org

6, 30, 114, 486, 1986, 8202, 33858, 140262, 580938, 2407710, 9980394, 41384106, 171634482, 711932538, 2953394214, 12253006566, 50838740046, 210946278126, 875324356398, 3632308990686, 15073375131306, 62553271396074

Offset: 1

Michel Marcus, Apr 23 2020

nonn

Nathan Clisby, Endless self-avoiding walks, arXiv:1302.2796 [cond-mat.stat-mech], 2013. See Table 4 p. 23.

Cf. A334322, A334326, A334330, A334332, A334333, A334334.

A334332 Number of endless self-avoiding walks of length n for the union jack lattice.

Original entry on oeis.org

8, 56, 296, 1816, 10728, 62648, 365464, 2130488, 12424112, 72464136, 422680024, 2465699704, 14384367304, 83919450272, 489611186736, 2856635570680, 16667509269248, 97251708586688

Offset: 1

Michel Marcus, Apr 23 2020

Cf. A334322, A334326, A334330, A334331, A334333, A334334.

A334333 Number of endless self-avoiding walks of length n for the body centered cubic lattice.

Original entry on oeis.org

8, 56, 344, 2312, 14648, 96152, 622616, 4066376, 26456024, 172470776, 1124590904, 7328945336, 47829176312, 311758824440, 2035191240584, 13269735071816, 86634355605416, 565037351668904

Offset: 1

Michel Marcus, Apr 23 2020

Nathan Clisby, Endless self-avoiding walks, arXiv:1302.2796 [cond-mat.stat-mech], 2013. See Table 4 p. 23.

Cf. A334322, A334326, A334330, A334331, A334332, A334334.

A334334 Number of endless self-avoiding walks of length n for the face centered cubic lattice.

Original entry on oeis.org

12, 132, 1284, 12756, 126612, 1265604, 12652932, 126616404, 1267690812, 12697464132, 127218134748, 1274923451364, 12779117065740, 128110554439020

Offset: 1

Michel Marcus, Apr 23 2020

Nathan Clisby, Endless self-avoiding walks, arXiv:1302.2796 [cond-mat.stat-mech], 2013. See Table 4 p. 23.

Cf. A334322, A334326, A334330, A334331, A334332, A334333.

A334323 Squared end-to-end distance of irreducible endless self-avoiding walks of length n for the square lattice.

Original entry on oeis.org

4, 32, 156, 640, 2380, 8304, 27580, 89216, 280980, 869360, 2649284, 7967808, 23722244, 69977040, 204845220, 595628032, 1721605028, 4950241488, 14167239268, 40376066560, 114635882508, 324361357936, 914912704060, 2573307218304, 7218778025700, 20201661701936, 56408010198948

Offset: 1

Michel Marcus, Apr 23 2020

nonn

Nathan Clisby, Endless self-avoiding walks, arXiv:1302.2796 [cond-mat.stat-mech], 2013. See Table 2 column er_n p. 22.

Cf. A334322, A334324, A334325.

Name amended by Scott R. Shannon, Sep 16 2020

A334324 Number of irreducible endless self-avoiding walks of length n for the square lattice.

Original entry on oeis.org

4, 8, 24, 64, 200, 504, 1400, 3648, 9720, 25560, 67936, 178464, 472576, 1244208, 3286080, 8663232, 22861600, 60291504, 159063744, 419556560, 1106794584, 2919596768, 7701735288, 20316965760, 53595401400, 141384847344, 372973574160, 983911970608, 2595592842456, 6847273559040

Offset: 1

Michel Marcus, Apr 23 2020

nonn

Nathan Clisby, Endless self-avoiding walks, arXiv:1302.2796 [cond-mat.stat-mech], 2013. See Table 2 column i_n p. 22.

Cf. A334322, A334323, A334325.

A334325 Number of irreducible, unrooted, unoriented self-avoiding chains of length n for the square lattice.

Original entry on oeis.org

2, 2, 4, 8, 20, 42, 100, 228, 540, 1278, 3088, 7436, 18176, 44436, 109536, 270726, 672400, 1674764, 4185888, 10488914, 26352252, 66354472, 167429028, 423270120, 1071908028, 2718939372, 6906918040, 17569856618, 44751600732, 114121225984, 291346481204, 744569863528

Offset: 1

Michel Marcus, Apr 23 2020

nonn

Nathan Clisby, Endless self-avoiding walks, arXiv:1302.2796 [cond-mat.stat-mech], 2013. See Table 2 column d_n p. 22.

Cf. A334322, A334323, A334324.

A334398 Number of endless self-avoiding walks of length n for the square lattice up to rotation, reflection, and path reversal.

Original entry on oeis.org

1, 2, 3, 7, 16, 39, 96, 245, 631, 1642

Offset: 1

Peter Kagey and Arnauld Chevallier, Apr 26 2020

a(n) > A334322(n)/16.

			The a(4) = 7 step patterns of length 4 are
---->---->---->---->, ---->---->---->, ---->---->     ,
                                    |           |
                                    v           v---->
---->---->, ---->    ^, ---->     , and ---->     .
         |      |    |      |               |
         v      v---->      v---->          v
         |                       |          |
         v                       v          v---->

Nathan Clisby, Endless self-avoiding walks, arXiv:1302.2796 [cond-mat.stat-mech], 2013.
Code Golf Stack Exchange, Infinite Snake game

Cf. A334322.

cp's OEIS Frontend

A334326 Number of endless self-avoiding walks of length n on the simple cubic lattice.

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A334330 Number of endless self-avoiding walks of length 2*n for the honeycomb lattice.

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A334331 Number of endless self-avoiding walks of length n on the triangular lattice.

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A334332 Number of endless self-avoiding walks of length n for the union jack lattice.

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A334333 Number of endless self-avoiding walks of length n for the body centered cubic lattice.

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A334334 Number of endless self-avoiding walks of length n for the face centered cubic lattice.

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A334323 Squared end-to-end distance of irreducible endless self-avoiding walks of length n for the square lattice.

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A334324 Number of irreducible endless self-avoiding walks of length n for the square lattice.

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A334325 Number of irreducible, unrooted, unoriented self-avoiding chains of length n for the square lattice.

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A334398 Number of endless self-avoiding walks of length n for the square lattice up to rotation, reflection, and path reversal.

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