A362298 Number of tilings of a 4 X n rectangle using dominos and 2 X 2 right triangles.

1, 1, 19, 55, 472, 2023, 13249, 66325, 392299, 2088856, 11877025, 64803157, 362823607, 1998759703, 11123273896, 61509329983, 341492705365, 1891193243713, 10489893539203, 58127214942544, 322296397820593, 1786338231961609, 9903234373856059, 54893955008138983

Offset: 0

Author

Gerhard Kirchner, Apr 19 2023

Keywords

• nonn
• easy

Comments

Triangles only occur as pairs forming 2 X 2 squares. For program code and additional details, see A362297.

Examples

			a(2) = 19.
Partitions of a 2 X 2 square (triangles or dominos):
   ___    ___    ___    ___
  |  /|  |\  |  |___|  | | |
  |/__|  |__\|  |___|  |_|_|
       2t            2d
   ___ ___    ___ ___    ___ ___    _ ___ _    _______
  |2t |2t |  |2t |2d |  |2d |2t |  | |2t | |  |only d |
  |___|___|  |___|___|  |___|___|  |_|___|_|  |_______|
    4 ways +   4 ways +  4 ways  +   2 ways +  5 ways  = 19 ways
Only dominos: A005178(3) = 5.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (4,18,-48,-42,99).

Crossrefs

Column k=2 of A362297.

Cf. A351322, A352432, A352433, A006130, A362299.

Programs

Mathematica

LinearRecurrence[{4,18,-48,-42,99},{1,1,19,55,472},24] (* Stefano Spezia, Apr 20 2023 *)

Formula

a(n) = 4*a(n-1) + 18*a(n-2) - 48*a(n-3) - 42*a(n-4) + 99*a(n-5).

G.f.: (9*x^3-3*x^2-3*x+1)/(-99*x^5+42*x^4+48*x^3-18*x^2-4*x+1).