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.

A350819 Array read by antidiagonals: T(m,n) is the number of maximum independent sets in the 2m X 2n king graph.

Original entry on oeis.org

1, 1, 1, 1, 4, 1, 1, 12, 12, 1, 1, 32, 79, 32, 1, 1, 80, 408, 408, 80, 1, 1, 192, 1847, 3600, 1847, 192, 1, 1, 448, 7698, 26040, 26040, 7698, 448, 1, 1, 1024, 30319, 166368, 281571, 166368, 30319, 1024, 1, 1, 2304, 114606, 976640, 2580754, 2580754, 976640, 114606, 2304, 1
Offset: 0

Views

Author

Andrew Howroyd, Jan 17 2022

Keywords

Comments

Number of ways to tile a (2m+1) X (2n+1) board with m*n 2 X 2 tiles and 2m+2n+1 1 X 1 tiles.
For m,n > 0, T(m,n) is the number of minimum dominating sets in the (3m-1) X (3n-1) king graph.

Examples

			Table begins:
=============================================
m\n | 0   1    2      3       4        5
----+----------------------------------------
  0 | 1   1    1      1       1        1 ...
  1 | 1   4   12     32      80      192 ...
  2 | 1  12   79    408    1847     7698 ...
  3 | 1  32  408   3600   26040   166368 ...
  4 | 1  80 1847  26040  281571  2580754 ...
  5 | 1 192 7698 166368 2580754 32572756 ...
  ...

Links

Crossrefs

Rows 0..12 are A000012, A001787(n+1), A061593, A061594, A173782, A173783, A174154, A174155, A174558, A195648, A195649, A195650, A195651.
Main diagonal is A018807.
Cf. A350815, A350818.

Formula

T(m,n) = T(n,m).
T(m,n) = A350818(2*m, 2*n) = A350815(3*m-1, 3*n-1).

A195655 Number of ways to place 11n nonattacking kings on a 22 X 2n cylindrical chessboard.

Original entry on oeis.org

24576, 106500, 565512, 3392964, 22327496, 158877948, 1212120160, 9849731140, 84719304384, 766319864440, 7241521734020, 71028444904044, 718816489322444, 7466044767879028, 79230397598482712, 855840660674700612, 9381236750764316676, 104090420921618696952
Offset: 1

Views

Author

Vaclav Kotesovec, Sep 22 2011

Keywords

Comments

This cylinder is horizontal: a chessboard where it is supposed that rows 1 and 2n are in contact (number of columns = 22, number of rows = 2n).

Links

Crossrefs

Cf. A137432, A195653, A195654, A195650, A195660.

Formula

Recurrence order is 1829.

A195660 Number of ways to place 11n nonattacking kings on a vertical cylinder 22 X 2n.

Original entry on oeis.org

4096, 433500, 11682296, 153802520, 1301236304, 8155899320, 41180193352, 176740657340, 668845118276, 2290966142762, 7241521734020, 21437333168798, 60123048359816, 161217291701134, 416373921218580, 1041997475699102, 2539265644237492, 6050425313244116
Offset: 1

Views

Author

Vaclav Kotesovec, Sep 22 2011

Keywords

Comments

Vertical cylinder: a chessboard where it is supposed that the columns 1 and 22 are in contact (number of columns = 22, number of rows = 2n).

Links

Crossrefs

Cf. A195655, A195650, A137432.

Formula

Recurrence: a(n) = -4*a(n-12) + 44*a(n-11) - 221*a(n-10) + 670*a(n-9) - 1365*a(n-8) + 1968*a(n-7) - 2058*a(n-6) + 1572*a(n-5) - 870*a(n-4) + 340*a(n-3) - 89*a(n-2) + 14*a(n-1).
G.f.: (1 + 4082*x + 376245*x^2 + 5977500*x^3 + 27440106*x^4 + 43897316*x^5 + 25742850*x^6 + 5340248*x^7 + 353057*x^8 + 5622*x^9 + 23*x^10)/((x-1)^10*(2*x-1)^2).
a(n) = (4480441703*n - 59644067185)*2^n + 10913705/36288*n^9 + 219791627/20160*n^8 + 6663742261/30240*n^7 + 1542837967/480*n^6 + 314791170001/8640*n^5 + 311982683023/960*n^4 + 6333872421866/2835*n^3 + 56561301500209/5040*n^2 + 46445710897861/1260*n + 59644067186.
Showing 1-3 of 3 results.

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