cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A259804 Guttmann-Torrie series coefficients rho_n*c_{n}^{2} for square lattice, with wedge angle Pi/4.

Original entry on oeis.org

1, 6, 19, 68, 190, 610, 1618, 4870, 12776, 37270, 97264, 277858, 723856, 2039120, 5309076, 14805780, 38549984, 106693682, 277890081, 764597138, 1992327855, 5456154914, 14224333948, 38806355844, 101220914578, 275278038948, 718383950316, 1948531080114
Offset: 1

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Author

N. J. A. Sloane, Jul 06 2015

Keywords

Comments

The sum of square end-to-end distance of all n-step self-avoiding walks on a 2D square lattice confined to one octant of the grid. - Scott R. Shannon, Sep 26 2021

References

  • A. J. Guttmann and G. M. Torrie, Critical behavior at an edge for the SAW and Ising model, J. Phys. A 17 (1984), 3539-3552.

Crossrefs

Cf. A129700 (number of SAWs in octant grid).

Extensions

a(23)-a(28) from Scott R. Shannon, Sep 26 2021

A348057 Number of n-step self-avoiding walks on three quadrants of a 2D square lattice.

Original entry on oeis.org

1, 4, 10, 28, 74, 202, 534, 1442, 3822, 10258, 27202, 72718, 192840, 514228, 1363342, 3629316, 9619264, 25575326, 67765590, 180001304, 476807826, 1265567600, 3351529410, 8890447682, 23538665948, 62409037914, 165202281046
Offset: 0

Views

Author

Scott R. Shannon, Sep 26 2021

Keywords

Examples

			a(2) = 10. Assuming the lower left quadrant is the one removed then a walk of left-down or down-left is not permitted, so the total number of 2-step walks is 4 * 3 - 2 = 10.

Crossrefs

Cf. A001411 (four quadrants), A116903 (two quadrants), A038373 (one quadrant), A129700 (half quadrant).
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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