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 1-5 of 5 results.

A151523 Number of 1-sided strip polyrhombs with n cells.

Original entry on oeis.org

1, 2, 4, 10, 20, 48, 106, 252, 578, 1372, 3208, 7584, 17850, 42102, 99276, 233716, 550960, 1295146, 3050226, 7161346, 16846668, 39511876, 92845830
Offset: 1

Views

Author

Ed Pegg Jr, May 13 2009

Keywords

Comments

Also counts 1-sided strip polyrects.

Links

Crossrefs

Strip polyominoes by group of symmetries relating shapes considered the same: A002013 (all symmetries), A182644 (translations only), A151514 (rotations and translations), A151527 (horizontal and vertical reflections, rotations of order 2 and translations), A151524 (reflections in either diagonal, rotations of order 2 and translations), A151523 (rotations of order 2 and translations), A151526 (reflections in a horizontal line and translations), A182646 (reflections in a NE-SW diagonal line and translations)

Extensions

Edited and a(15)-a(23) by Joseph Myers, Nov 24 2010

A151526 Number of strip poly-IH64-tiles (holes allowed) with n cells.

Original entry on oeis.org

1, 2, 4, 8, 19, 43, 103, 239, 569, 1339, 3185, 7503, 17794, 41908, 99137, 233251, 550624, 1294032, 3049412, 7158698, 16844717, 39505579, 92841149
Offset: 1

Views

Author

Ed Pegg Jr, May 13 2009

Keywords

Comments

Equivalently, strip polyominoes where two polyominoes are considered the same if and only if they are related by a translation or a reflection in a horizontal line. Formerly described as one-sided strip polyrects, but that is A151523.

References

  • Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987, Sections 6.2 and 9.4.

Crossrefs

Strip polyominoes by group of symmetries relating shapes considered the same: A002013 (all symmetries), A182644 (translations only), A151514 (rotations and translations), A151527 (horizontal and vertical reflections, rotations of order 2 and translations), A151524 (reflections in either diagonal, rotations of order 2 and translations), A151523 (rotations of order 2 and translations), A151526 (reflections in a horizontal line and translations), A182646 (reflections in a NE-SW diagonal line and translations)

Extensions

Edited and a(15)-a(23) by Joseph Myers, Nov 24 2010

A182646 Number of strip poly-IH68-tiles (holes allowed) with n cells.

Original entry on oeis.org

1, 1, 4, 7, 19, 41, 104, 235, 572, 1331, 3193, 7485, 17811, 41867, 99181, 233157, 550718, 1293817, 3049649, 7158201, 16845217, 39504435, 92842398
Offset: 1

Views

Author

Joseph Myers, Nov 24 2010

Keywords

Comments

Equivalently, strip polyominoes where two polyominoes are considered the same if and only if they are related by a translation or a reflection in a NE-SW diagonal line.

References

  • Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987, Sections 6.2 and 9.4.

Crossrefs

Strip polyominoes by group of symmetries relating shapes considered the same: A002013 (all symmetries), A182644 (translations only), A151514 (rotations and translations), A151527 (horizontal and vertical reflections, rotations of order 2 and translations), A151524 (reflections in either diagonal, rotations of order 2 and translations), A151523 (rotations of order 2 and translations), A151526 (reflections in a horizontal line and translations), A182646 (reflections in a NE-SW diagonal line and translations)

A118339 Number of simple chains with n-1 edges strongly embedded in a simple cubic lattice.

Original entry on oeis.org

1, 3, 15, 63, 267, 1107, 4623, 19071, 78987, 324543, 1337511, 5483235, 22527315, 92200455, 377965479, 1544925891, 6322891707
Offset: 1

Views

Author

R. J. Mathar, May 14 2006

Keywords

Comments

Gaunt et al. also enumerate clusters with upper limits on the vertex degree.
a(n) is the number of fixed linear or snake polycubes of size n. - John Mason, Sep 27 2024

Links

Crossrefs

Cf. A182644, A363201, A363202.

A367557 The number of fixed kissing polyominoes with n cells.

Original entry on oeis.org

4, 40, 260, 1428, 7184, 34238, 157398, 705518, 3104394, 13469766, 57811669, 245990766
Offset: 7

Views

Author

Johann Peters, Nov 22 2023

Keywords

Comments

Translations are allowed, but not rotations or reflections.
A polyomino is 'kissing' if there exist two cells that touch only at a corner such that no cell exists touching both edgewise simultaneously.
First thirteen terms calculated by filtering the output of Redelmeier's Algorithm.

Examples

			The smallest kissing polyomino has area 7; its four rotations determine the first term in the sequence:
    OOO
    O O
    OO

Links

Crossrefs

Cf. A182644, A376496.

Extensions

a(14)-a(18) from John Mason, Sep 25 2024
Showing 1-5 of 5 results.

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

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