A354012 Number of tilings of a 4 X n rectangle using 2 X 2 tiles, right trominoes and dominoes.

1, 1, 17, 81, 702, 4623, 35044, 248045, 1819731, 13110984, 95362462, 690253391, 5008926698, 36300216768, 263252448712, 1908449014617, 13837881924141, 100326715619679, 727420462629671, 5274035027493046, 38238994112367061, 277246970248002472, 2010151423463689959

Offset: 0

Author

Gerhard Kirchner, May 14 2022

Keywords

• nonn
• easy

Comments

For tiling algorithm, see A351322.

Examples

			a(2)=17, mirroring included (h: horizontal, v: vertical):
    v     v          h,v                      v           h
   ___   ___   ___   ___   ___   ___   ___   ___   ___   ___
  |   | |   | |   | |___| |___| | | | |___| |___| |___| |  _|
  |___| |___| |___| |_  | |___| |_|_| | | | |___| |   | |_| |
  |___| | | | |   | | |_| |___| | | | |_|_| | | | |___| | |_|
  |___| |_|_| |___| |___| |___| |_|_| |___| |_|_| |___| |___|
    2  +  2  +  1  +  4  +  1  +  1  +  1  +  2  +  1  +  2  = 17.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (5,28,-69,-142,194,78,-57,-36,70,-32).

Crossrefs

Cf. A351322, A352589, A354010, A354011.

Programs

Maxima

See A352589.

Formula

G.f.: (1 - 4*x - 16*x^2 + 37*x^3 + 32*x^4 - 34*x^5 + 4*x^6 + 2*x^7 - 2*x^8) / (1 - 5*x - 28*x^2 + 69*x^3 + 142*x^4 - 194*x^5 - 78*x^6 + 57*x^7 + 36*x^8 - 70*x^9 + 32*x^10).

a(n)=5*a(n-1) + 28*a(n-2) - 69*a(n-3) - 142*a(n-4) + 194*a(n-5) + 78*a(n-6) - 57*a(n-7) - 36*a(n-8) + 70*a(n-9) - 32*a(n-10).