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A335560 Number of ways to tile an n X n square with 1 X 1 squares and (n-1) X 1 vertical or horizontal strips. 2
1, 16, 131, 335, 851, 2207, 5891, 16175, 45491, 130367, 378851, 1112015, 3286931, 9762527, 29091011, 86879855, 259853171, 777986687, 2330814371, 6986151695, 20945872211, 62812450847, 188387020931, 565060399535, 1694979872051, 5084536963007, 15252805582691 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

It is assumed that 1 X 1 squares and 1 X 1 strips can be distinguished. - Alois P. Heinz, Feb 23 2022

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

FORMULA

a(n) = 2*3^n + 12*2^n - 19, for n >= 3.

From Colin Barker, Jun 14 2020: (Start)

G.f.: x*(1 + 10*x + 46*x^2 - 281*x^3 + 186*x^4) / ((1 - x)*(1 - 2*x)*(1 - 3*x)).

a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n>5.

(End)

EXAMPLE

Here is one of the 131 ways to tile a 3 X 3 square, in this case using two horizontal and two vertical strips:

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  |_ _| |

  | |_|_|

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MATHEMATICA

Join[{1, 16}, LinearRecurrence[{6, -11, 6}, {131, 335, 851}, 25]] (* Amiram Eldar, Jun 16 2020 *)

PROG

(PARI) Vec(x*(1 + 10*x + 46*x^2 - 281*x^3 + 186*x^4) / ((1 - x)*(1 - 2*x)*(1 - 3*x)) + O(x^30)) \\ Colin Barker, Jun 14 2020

CROSSREFS

Cf. A063443 and A211348 (tiling an n X n square with smaller squares).

Cf. A028420 (tiling an n X n square with monomers and dimers).

Sequence in context: A196595 A055914 A255816 * A253224 A334979 A183535

Adjacent sequences:  A335557 A335558 A335559 * A335561 A335562 A335563

KEYWORD

nonn,easy

AUTHOR

Oluwatobi Jemima Alabi, Jun 14 2020

STATUS

approved

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Last modified May 25 12:00 EDT 2022. Contains 354071 sequences. (Running on oeis4.)