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 1-3 of 3 results.

A008855 Triangle T(n,k), n>=1, read by rows, where T(n,k) is the number of lattice polygons with area n and perimeter 2*k.

Original entry on oeis.org

1, 2, 6, 1, 18, 8, 55, 2, 40, 174, 22, 168, 566, 6, 134, 676, 1868, 1, 72, 656, 2672, 6237, 30, 482, 2992, 10376, 21050, 8, 310, 2592, 13160, 39824, 71666, 2, 151, 2086, 12862, 56162, 151878, 245696, 68, 1392, 11717, 61032, 234520, 576656, 847317, 22, 864, 9332, 60864, 279492, 965136, 2181496, 2937116
Offset: 1

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Keywords

Comments

Row lengths are 1, 1, 1, 2, 2, 3, 3, 4, 5, 5, ...

Examples

			T(1,2) = 1;
   +--+
   |  |
   +--+
T(2,3) = 2;
   +--+
   |  |
   +--+   +--+--+
   |  |   |  |  |
   +--+   +--+--+
T(3,4) = 6;
   +--+
   |  |
   +--+                +--+
   |  |                |  |
   +--+   +--+--+--+   +--+--+
   |  |   |  |  |  |   |  |  |
   +--+   +--+--+--+   +--+--+
      +--+   +--+--+   +--+--+
      |  |   |  |  |   |  |  |
   +--+--+   +--+--+   +--+--+
   |  |  |   |  |         |  |
   +--+--+   +--+         +--+
============================================
n\k | 2  3  4   5   6    7    8     9    10
----|---------------------------------------
  1 | 1;
  2 |    2;
  3 |       6;
  4 |       1, 18;
  5 |           8, 55;
  6 |           2, 40, 174;
  7 |              22, 168, 566;
  8 |               6, 134, 676, 1868;
  9 |               1,  72, 656, 2672, 6237;
		

Crossrefs

Extensions

More terms from Sean A. Irvine, Apr 12 2018
Examples added and name edited by Seiichi Manyama, Apr 04 2020

A034010 Number of 2n-step self avoiding closed walks on square grid, restricted to a quadrant and passing through origin.

Original entry on oeis.org

0, 1, 2, 6, 20, 74, 300, 1302, 5944, 28266, 139010, 703102, 3641956, 19255106, 103630920, 566522778, 3140130354, 17620845976, 99977635264, 572935630884, 3313078283974
Offset: 1

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Keywords

Examples

			When the number of steps is 8, one of the six closed paths is
0___.
| ._|
|_|
		

Crossrefs

A subset of the polyominoes with perimeter 2n (A006725), also a subset of A002931. Cf. A000105, A038373.

Extensions

Corrected and extended by David W. Wilson
a(16)-a(18) from Alex Chernov, Jan 22 2012
a(19)-a(21) from Bert Dobbelaere, Jan 06 2019

A259857 Triangle T(n,k), n>=1, 2<=k<=n+1, read by rows, where T(n,k) is the number of self-avoiding square-lattice polygons by area n and perimeter 2*k.

Original entry on oeis.org

1, 0, 2, 0, 0, 6, 0, 0, 1, 18, 0, 0, 0, 8, 55, 0, 0, 0, 2, 40, 174, 0, 0, 0, 0, 22, 168, 566, 0, 0, 0, 0, 6, 134, 676, 1868, 0, 0, 0, 0, 1, 72, 656, 2672, 6237, 0, 0, 0, 0, 0, 30, 482, 2992, 10376, 21050, 0, 0, 0, 0, 0, 8, 310, 2592, 13160, 39824, 71666, 0, 0, 0, 0, 0, 2, 151, 2086, 12862, 56162, 151878, 245696
Offset: 1

Views

Author

N. J. A. Sloane, Jul 07 2015

Keywords

Examples

			Triangle begins:
==========================================================
n\k  | 2 3 4  5  6   7   8    9    10    11     12     13
-----|----------------------------------------------------
   1 | 1,
   2 | 0,2,
   3 | 0,0,6,
   4 | 0,0,1,18
   5 | 0,0,0, 8,55,
   6 | 0,0,0, 2,40,174,
   7 | 0,0,0, 0,22,168,566,
   8 | 0,0,0, 0, 6,134,676,1868,
   9 | 0,0,0, 0, 1, 72,656,2672, 6237,
  10 | 0,0,0, 0, 0, 30,482,2992,10376,21050,
  11 | 0,0,0, 0, 0,  8,310,2592,13160,39824, 71666,
  12 | 0,0,0, 0, 0,  2,151,2086,12862,56162,151878,245696,
		

Crossrefs

A006725 and A006726 are diagonals.
Row sums give A006724.
Cf. A008855 (with 0 omitted).

Extensions

a(7)-a(10) inserted by Seiichi Manyama, Apr 04 2020
Showing 1-3 of 3 results.