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.

A353964 Number of tilings of a 2 X n rectangle using 2 X 2 and 1 X 1 tiles and right trominoes.

Original entry on oeis.org

1, 1, 6, 13, 45, 122, 373, 1073, 3182, 9293, 27349, 80178, 235509, 691097, 2028998, 5955501, 17482685, 51318186, 150642613, 442198913, 1298048350, 3810328141, 11184967717, 32832705122, 96378199989, 282911661033, 830468071222, 2437782776365, 7155946454541
Offset: 0

Views

Author

Gerhard Kirchner, May 13 2022

Keywords

Comments

For tiling algorithm see A351322.

Examples

			a(3)=13, see example 3 X 2, A353965.
		

Crossrefs

Programs

Formula

G.f.: 1 / (1 - x - 5*x^2 - 2*x^3).
a(n) = a(n-1) + 5*a(n-2) + 2*a(n-3).

A353965 Number of tilings of a 3 X n rectangle using 2 X 2 and 1 X 1 tiles and right trominoes.

Original entry on oeis.org

1, 1, 13, 47, 259, 1189, 5877, 28167, 136723, 660173, 3194613, 15445007, 74699811, 361230229, 1746933205, 8448061879, 40854753875, 197572345789, 955455626773, 4620559362303, 22344915889827, 108059470995013, 522573007884725, 2527150465444071, 12221238828079379
Offset: 0

Views

Author

Gerhard Kirchner, May 13 2022

Keywords

Comments

For tiling algorithm see A351322.

Examples

			a(2) = 13:
    v    h,v   h=v   h,v
   ___   ___   ___   ___   ___
  |   | | |_| |  _| |  _| |_|_|    mirroring included
  |___| |___| |_| | |_|_| |_|_|    h: horizontal, v: vertical
  |_|_| |_|_| |___| |_|_| |_|_|
    2  +  4  +  2  +  4  +  1 = 13
		

Crossrefs

Programs

Formula

G.f.: (1 - 2*x + x^2) / (1 - 3*x - 9*x^2 + x^3 - 2*x^4).
a(n) = 3*a(n-1) + 9*a(n-2) - a(n-3) + 2*a(n-4).
31*a(n) = 18*(-2)^n +13*A200739(n+3) +2*A200739(n+2) +9*A200739(n+1). - R. J. Mathar, Jun 07 2025

A354067 Number of tilings of an n X n square using right trominoes, monominoes and 2 X 2 tiles.

Original entry on oeis.org

1, 1, 6, 47, 3376, 475962, 355724934, 777719132265, 6953251175836902, 211458363740571796706, 24140111818602303894344572, 9821069154293248979055457847110, 14628885986751823763315761493151275720, 78680004562091421665338332919348995334919722
Offset: 0

Views

Author

Alois P. Heinz, May 16 2022

Keywords

Examples

			a(2) = 6:
  .___.  .___.  .___.  .___.  .___.  .___.
  | |_|  | ._|  |_. |  |_| |  |_|_|  |   |
  |___|  |_|_|  |_|_|  |___|  |_|_|  |___| .
		

Crossrefs

Main diagonal of A353963.

Formula

a(n) = A353963(n,n).
Showing 1-3 of 3 results.