A352433 Number of tilings of a 5 X 2n rectangle using dominoes and 2 X 2 tiles.

1, 21, 593, 17937, 550969, 16982489, 523857737, 16162268361, 498665065833, 15385785653481, 474713270165161, 14646818304387753, 451913453451818281, 13943354204817352489, 430208763273959521833, 13273677023152591308329, 409546519819086706020393

Offset

0,2

Comments

The sequence is based on A352431.

Links

Table of n, a(n) for n=0..16.

Index entries for linear recurrences with constant coefficients, signature (51,-764,4822,-13756,17328,-7680). [Signs corrected by Georg Fischer, Sep 30 2022]

Formula

G.f.: (1 - 30*x + 286*x^2 - 1084*x^3 + 1728*x^4 - 960*x^5)/(1 - 51*x + 764*x^2 - 4822*x^3 + 13756*x^4 - 17328*x^5 + 7680*x^6).

a(n) = 51*a(n-1) - 764*a(n-2) + 4822*a(n-3) - 13756*a(n-4) + 17328*a(n-5) - 7680*a(n-6).

Example

n=1: a(1)=21
The cells in the first row are covered by a horizontal domino, vertical dominoes or a square. The remaining rectangle has 11 (see example A352432) or 5 tilings.
   ___    ___    ___                5 tilings of a 3 X 2 rectangle:
  |___|  | | |  |   |                 ___   ___   ___   ___   ___
  |   |  |_|_|  |___|                |   | |___| |___| | | | |___|
  |   |  |   |  |   |                |___| |   | |___| |_|_| |___|
  | 11|  | 5 |  | 5 |                |___| |___| |___| |___| |_|_|
  |___|  |___|  |___|

Mathematica

LinearRecurrence[{51, -764, 4822, -13756, 17328, -7680}, {1, 21, 593, 17937, 550969, 16982489}, 17] (* Hugo Pfoertner, Sep 30 2022 *)

Prog

(PARI) Vec((1-30*x+286*x^2-1084*x^3+1728*x^4-960*x^5)/(1-51*x+764*x^2-4822*x^3+13756*x^4-17328*x^5+7680*x^6)+O(x^99)) \\ Charles R Greathouse IV, Jul 05 2024

Crossrefs

Cf. A352431, A352432.

Sequence in context: A199199 A089457 A265631 * A009091 A231639 A159278

Adjacent sequences: A352430 A352431 A352432 * A352434 A352435 A352436

Keyword

nonn,easy

Author

Gerhard Kirchner, Mar 17 2022

Status

approved