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.

Previous Showing 11-13 of 13 results.

A259802 Guttmann-Torrie series coefficients rho_n*c_{n}^{2} for square lattice, with wedge angle Pi/2.

Original entry on oeis.org

2, 12, 50, 188, 652, 2140, 6766, 20868, 63118, 188004, 553074, 1610776, 4651784, 13338744, 38014494, 107767964, 304100432, 854624852, 2393093804, 6679440288, 18589013256, 51597951784, 142880148016, 394791197276, 1088674291748, 2996639940048
Offset: 1

Views

Author

N. J. A. Sloane, Jul 06 2015

Keywords

Comments

The sum of squared end-to-end distances of all n-step self-avoiding walks on a 2D square lattice confined to one quadrant of the grid. - Scott R. Shannon, Sep 27 2021

Links

Crossrefs

Cf. A038373 (number of SAWs in quadrant grid).

Extensions

a(23)-a(26) from Scott R. Shannon, Sep 27 2021

A336988 Table read by antidiagonals: T(h,n) is the number of n-step self avoiding walks on a 2D square grid confined to an infinite strip of height 2h where the walk starts at coordinate (0,h).

Original entry on oeis.org

4, 10, 4, 22, 12, 4, 42, 34, 12, 4, 90, 82, 36, 12, 4, 182, 194, 98, 36, 12, 4, 382, 438, 262, 100, 36, 12, 4, 742, 1034, 650, 282, 100, 36, 12, 4, 1486, 2362, 1610, 754, 284, 100, 36, 12, 4, 2866, 5558, 3870, 1994, 778, 284, 100, 36, 12, 4
Offset: 1

Views

Author

Scott R. Shannon, Aug 10 2020

Keywords

Examples

			T(1,3) = 22. The five 3-step walks taking a first step to the right and upward or a step upward and then to the right are:
.
      +  +--+     +--+  +--+--+  +--+
      |     |     |     |        |  |
X--+--+  X--+  X--+     X        X  +
.
The same steps can be taken to the right then down, to the left then down, and to the left then up. There is also the two straight walks right and left. This give a total number of walks of 4*5+2 = 22.
.
The table begins:
.
4 10 22  42  90 182  382  742  1486  2866   5646  10878  21198   40694   78758...
4 12 34  82 194 438 1034 2362  5558 12662  29366  66330 151566  339514  767798...
4 12 36  98 262 650 1610 3870  9490 22830  55826 134242 326934  784770 1901246...
4 12 36 100 282 754 1994 5046 12786 31746  79566 196858 491506 1214262 3024890...
4 12 36 100 284 778 2142 5682 14986 38462  98762 249894 635290 1599394 4048366...
4 12 36 100 284 780 2170 5882 15970 42286 111554 288962 748414 1916762 4921146...
4 12 36 100 284 780 2172 5914 16230 43730 117810 311894 823682 2146886 5593690...
4 12 36 100 284 780 2172 5916 16266 44058 119842 321630 862674 2284682 6040622...
4 12 36 100 284 780 2172 5916 16268 44098 120246 324394 877210 2348022 6281498...
4 12 36 100 284 780 2172 5916 16268 44100 120290 324882 880866 2368982 6380418...
4 12 36 100 284 780 2172 5916 16268 44100 120292 324930 881446 2373706 6409762...
4 12 36 100 284 780 2172 5916 16268 44100 120292 324932 881498 2374386 6415746...
4 12 36 100 284 780 2172 5916 16268 44100 120292 324932 881500 2374442 6416534...
4 12 36 100 284 780 2172 5916 16268 44100 120292 324932 881500 2374444 6416594...
4 12 36 100 284 780 2172 5916 16268 44100 120292 324932 881500 2374444 6416596...

Crossrefs

Cf. A336769 (start at origin), A001411 (h->infinity), A007825 (h=1), A116903, A038373, A336863, A336818.

Formula

For n <= h, T(h,n) = A001411(n).
Row 1 = T(1,n) = A007825(n).

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).
Previous Showing 11-13 of 13 results.

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

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