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.

A288026 Array read by antidiagonals: T(m,n) = number of maximal matchings in the grid graph P_m X P_n.

Original entry on oeis.org

1, 1, 1, 2, 2, 2, 2, 5, 5, 2, 3, 11, 22, 11, 3, 4, 24, 75, 75, 24, 4, 5, 51, 264, 400, 264, 51, 5, 7, 109, 941, 2357, 2357, 941, 109, 7, 9, 234, 3286, 13407, 22228, 13407, 3286, 234, 9, 12, 503, 11623, 76667, 207423, 207423, 76667, 11623, 503, 12
Offset: 1

Views

Author

Andrew Howroyd, Jun 04 2017

Keywords

Examples

			Table starts:
=====================================================
m\n| 1   2    3     4       5        6          7
---|-------------------------------------------------
1  | 1   1    2     2       3        4          5 ...
2  | 1   2    5    11      24       51        109 ...
3  | 2   5   22    75     264      941       3286 ...
4  | 2  11   75   400    2357    13407      76667 ...
5  | 3  24  264  2357   22228   207423    1922112 ...
6  | 4  51  941 13407  207423  3136370   47256485 ...
7  | 5 109 3286 76667 1922112 47256485 1158560776 ...
...

Links

Crossrefs

Main diagonal is A287595.
Rows 1-3 are A182097(n+2), A286945, A288028.
Cf. A210662, A099390, A286912, A288025.

A288028 Number of maximal matchings in the grid graph P_3 X P_n.

Original entry on oeis.org

2, 5, 22, 75, 264, 941, 3286, 11623, 40960, 144267, 508812, 1792981, 6319994, 22277291, 78518760, 276763545, 975517878, 3438444583, 12119670866, 42718700667, 150572583140, 530730064095, 1870688029160, 6593699432859, 23241110692298, 81918995835971
Offset: 1

Views

Author

Andrew Howroyd, Jun 04 2017

Keywords

Links

Crossrefs

Row 3 of A288026.
Cf. A286945, A287595.

Formula

Empirical: a(n) = a(n-1) +5*a(n-2) +11*a(n-3) +5*a(n-4) +14*a(n-5) +8*a(n-6) +3*a(n-7) -5*a(n-9) -11*a(n-10) -a(n-11) +2*a(n-12) +a(n-15) for n>15.
Empirical g.f.: x*(2 +3*x +7*x^2 +6*x^3 +14*x^4 +7*x^5 +4*x^6 -x^7 -5*x^8 - 11*x^9 -2*x^10 +2*x^11 +x^12 +x^14)/(1 -x -5*x^2 -11*x^3 -5*x^4 -14*x^5 - 8*x^6 -3*x^7 +5*x^9 +11*x^10 +x^11 -2*x^12 -x^15). - Colin Barker, Jun 11 2017

A332865 Number of placements of zero or more dominoes on the n X n grid where no two empty squares are horizontally adjacent.

Original entry on oeis.org

1, 4, 48, 1427, 140555, 40008789, 33656587715, 84588476099284, 626461671945179295, 13776144517953719025396, 897220763259635483826935324, 173109540246969825014223808529273, 98978509126162805673620043358494745638, 167661422725328648892707605323564506782035252
Offset: 1

Views

Author

Neil A. McKay, Feb 27 2020

Keywords

Comments

The number of positions of n X n Domineering where horizontal (Right) has no moves, also called Right ends. Domineering is a game in which players take turns placing dominoes on a grid, one player placing vertically and the other horizontally until the player to place cannot place a domino.

Links

Crossrefs

Main diagonal of A332862.
Cf. A287595 (the number of placements of dominoes on an n X n grid where no two empty squares are horizontally or vertically adjacent).
Cf. A332714.

Programs

  • Sage
    # See Bjorn Huntemann, Svenja Huntemann, Neil A. McKay link.

Extensions

a(9)-a(14) from Andrew Howroyd, Feb 28 2020
Showing 1-3 of 3 results.

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

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