A362299 Number of tilings of a 3 X 2n rectangle using dominos and 2 X 2 right triangles.

1, 7, 55, 445, 3625, 29575, 241375, 1970125, 16080625, 131254375, 1071334375, 8744528125, 71375265625, 582584734375, 4755218359375, 38813412578125, 316805850390625, 2585857315234375, 21106485396484375, 172276994236328125, 1406172661416015625

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(1)=7:
   ___ _    _ ___    ___ _    _ ___    ___ _    _ ___    ___ _
  |  /| |  | |  /|  |\  | |  | |\  |  |___| |  | |___|  | | | |
  |/__|_|  |_|/__|  |__\|_|  |_|__\|  |___|_|  |_|___|  |_|_|_|
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-15).

Crossrefs

Row n=3 of A362297.

Cf. A351322, A352432, A352433, A006130, A362298.

Programs

Mathematica

LinearRecurrence[{10, -15}, {1, 7}, 30] (* Paolo Xausa, Jul 20 2024 *)

Formula

a(n) = 10*a(n-1) - 15*a(n-2).

G.f.: (1 - 3*x)/(1 - 10*x + 15*x^2).

E.g.f.: exp(5*x)*(5*cosh(sqrt(10)*x) + sqrt(10)*sinh(sqrt(10)*x))/5. - Stefano Spezia, Apr 20 2023