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 1-10 of 11 results. Next

A005519 Let T(n,d) = number of distinct d-dimensional polyominoes (or polycubes) with n cells (A049429, A049430); sequence gives Sum_{d} T(n,d).

Original entry on oeis.org

1, 1, 2, 7, 26, 153, 1134, 11050, 128987, 1765252, 27418060
Offset: 1

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Author

N. J. A. Sloane

Keywords

Comments

These are free polyominoes, meaning that they are counted up to rotation, reflection, and translation. - Peter Kagey, Apr 30 2020

References

  • Dan Hoey, Bill Gosper and Richard C. Schroeppel, Discussions in Math-Fun Mailing list, circa Jul 13 1999.
  • W. F. Lunnon, personal communication.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Row sums of A049429 or A049430.

Extensions

a(9) from Richard C. Schroeppel
a(10) and a(11) from Peter Kagey, Apr 30 2020, based on the rows John Niss Hansen added to A049430

A068870 Number of polyhypercubes or 4-dimensional polyominoes with n cells (regarding mirror-images as identical).

Original entry on oeis.org

1, 1, 1, 2, 7, 26, 147, 1019, 8699, 82535, 846042, 9078720
Offset: 0

Views

Author

Franklin T. Adams-Watters, Mar 29 2002

Keywords

Links

Crossrefs

Excluding a(0), 140th row of A366766.
Cf. A049429, A049430, A255487.

Extensions

a(10) and a(11) from Don Reble, Feb 25 2015. - N. J. A. Sloane, Mar 01 2015

A049430 Triangle read by rows: T(n,d) is the number of distinct properly d-dimensional polyominoes (or polycubes) with n cells (n >= 1, d >= 0).

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 1, 4, 2, 0, 1, 11, 11, 3, 0, 1, 34, 77, 35, 6, 0, 1, 107, 499, 412, 104, 11, 0, 1, 368, 3442, 4888, 2009, 319, 23, 0, 1, 1284, 24128, 57122, 36585, 8869, 951, 47, 0, 1, 4654, 173428, 667959, 647680, 231574, 36988, 2862, 106, 0, 1, 17072, 1262464, 7799183, 11173880, 5712765, 1297366, 146578, 8516, 235
Offset: 1

Views

Author

Richard C. Schroeppel

Keywords

Examples

			Triangle begins:
1
0 1
0 1     1
0 1     4       2
0 1    11      11       3
0 1    34      77      35        6
0 1   107     499     412      104      11
0 1   368    3442    4888     2009     319      23
0 1  1284   24128   57122    36585    8869     951     47
0 1  4654  173428  667959   647680  231574   36988   2862  106
0 1 17072 1262464 7799183 11173880 5712765 1297366 146578 8516 235
...

Links

Crossrefs

Cf. A049429 (col. d=0 omitted), A195738 (oriented), A195739 (fixed).
Row sums give A005519. Columns give A006765, A006766, A006767, A006768.
Diagonals (with algorithms) are A000055, A036364, A355053.
Cf. A330891 (cumulative sums of the rows).

Extensions

Edited by N. J. A. Sloane, Sep 23 2011
More terms from John Niss Hansen, Mar 31 2015

A006765 Number of strictly 2-dimensional polyominoes with n cells.

Original entry on oeis.org

0, 0, 1, 4, 11, 34, 107, 368, 1284, 4654, 17072, 63599, 238590, 901970, 3426575, 13079254, 50107908, 192622051, 742624231, 2870671949, 11123060677, 43191857687, 168047007727, 654999700402, 2557227044763, 9999088822074, 39153010938486, 153511100594602, 602621953061977, 2368347037571251, 9317706529987949, 36695016991712878
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

A000105 is the main entry for this sequence.

References

  • Dan Hoey, Bill Gosper and Richard C. Schroeppel, Discussions in Math-Fun Mailing list, circa Jul 13 1999.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Equals A000105(n)-1. A row of A049429. A column of A049430.

Programs

Extensions

Edited by N. J. A. Sloane, Sep 23 2011
Name clarified by John Mason, Jan 10 2023

A330891 Triangle read by rows: cumulative sums of the rows of A049430.

Original entry on oeis.org

1, 0, 1, 0, 1, 2, 0, 1, 5, 7, 0, 1, 12, 23, 26, 0, 1, 35, 112, 147, 153, 0, 1, 108, 607, 1019, 1123, 1134, 0, 1, 369, 3811, 8699, 10708, 11027, 11050, 0, 1, 1285, 25413, 82535, 119120, 127989, 128940, 128987, 0, 1, 4655, 178083, 846042, 1493722, 1725296
Offset: 1

Views

Author

Peter Kagey, Apr 30 2020

Keywords

Comments

T(n,k) is also the number of n-celled polyominoes made up of k-dimensional cubes, counted up to rotation, reflection, and translation.

Examples

			Table begins:
n/k| 0 1    2     3     4      5      6      7      8
---+-------------------------------------------------
  1| 1
  2| 0 1
  3| 0 1    2
  4| 0 1    5     7
  5| 0 1   12    23    26
  6| 0 1   35   112   147    153
  7| 0 1  108   607  1019   1123   1134
  8| 0 1  369  3811  8699  10708  11027  11050
  9| 0 1 1285 25413 82535 119120 127989 128940 128987

Links

Crossrefs

Cf. A049429, A049430.
Columns 2-4: A000105, A038119, A068870.
Main diagonal is A005519.

Formula

T(n,k) = Sum_{i=0..k} A049430(n,i).

A006766 Number of 3-dimensional polyominoes with n cells.

Original entry on oeis.org

0, 0, 0, 2, 11, 77, 499, 3442, 24128, 173428, 1262464, 9307494
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • Dan Hoey, Bill Gosper and Richard C. Schroeppel, Discussions in Math-Fun Mailing list, circa Jul 13 1999.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

A row of A049429. A column of A049430.

A006768 Number of 5-dimensional polyominoes with n cells.

Original entry on oeis.org

0, 0, 0, 0, 0, 6, 104, 2009, 36585, 647680, 11173880
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • Dan Hoey, Bill Gosper and Richard C. Schroeppel, Discussions in Math-Fun Mailing list, circa Jul 13 1999.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

A row of A049429. A column of A049430.

Extensions

a(10)-a(11) from Sean A. Irvine, Jul 29 2017

A255487 Number of polyhypercubes or 4-dimensional polyominoes with n cells (regarding mirror-images as distinct).

Original entry on oeis.org

1, 1, 1, 2, 7, 27, 164, 1316, 12757, 134174, 1474341, 16588434
Offset: 0

Views

Author

N. J. A. Sloane, Mar 01 2015

Keywords

References

  • Don Reble, Personal communication, Feb 25 2015

Crossrefs

Cf. A049429, A049430, A068870.

Formula

a(n) = A006760(n) + A006765(n) + A006766(n) + signum(n-1) for n >= 1. - Sean A. Irvine, Jul 19 2017

A006767 Number of 4-dimensional polyominoes with n cells.

Original entry on oeis.org

0, 0, 0, 0, 3, 35, 412, 4888, 57122, 667959, 7799183
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • Dan Hoey, Bill Gosper and Richard C. Schroeppel, Discussions in Math-Fun Mailing list, circa Jul 13 1999.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

A row of A049429. A column of A049430.

A290305 Number of 5-dimensional polyominoes with n cells (regarding mirror-images as distinct).

Original entry on oeis.org

1, 1, 1, 2, 7, 26, 154, 1172, 12049, 148508, 2061893, 30545504
Offset: 0

Views

Author

Sean A. Irvine, Jul 26 2017

Keywords

Crossrefs

Cf. A049429, A049430, A006761 (one-sided), A255487 (4-dimensional case).

Formula

a(n) = A006761(n) + A068870(n).
Showing 1-10 of 11 results. Next

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

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