A354012 - OEIS

%I #11 May 17 2022 17:51:39

%S 1,1,17,81,702,4623,35044,248045,1819731,13110984,95362462,690253391,

%T 5008926698,36300216768,263252448712,1908449014617,13837881924141,

%U 100326715619679,727420462629671,5274035027493046,38238994112367061,277246970248002472,2010151423463689959

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

%C For tiling algorithm, see A351322.

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (5,28,-69,-142,194,78,-57,-36,70,-32).

%F 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).

%F 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).

%e a(2)=17, mirroring included (h: horizontal, v: vertical):

%e     v     v          h,v                      v           h

%e    ___   ___   ___   ___   ___   ___   ___   ___   ___   ___

%e   |   | |   | |   | |___| |___| | | | |___| |___| |___| |  _|

%e   |___| |___| |___| |_  | |___| |_|_| | | | |___| |   | |_| |

%e   |___| | | | |   | | |_| |___| | | | |_|_| | | | |___| | |_|

%e   |___| |_|_| |___| |___| |___| |_|_| |___| |_|_| |___| |___|

%e     2  +  2  +  1  +  4  +  1  +  1  +  1  +  2  +  1  +  2  = 17.

%o (Maxima) See A352589.

%Y Cf. A351322, A352589, A354010, A354011.

%K nonn,easy

%O 0,3

%A _Gerhard Kirchner_, May 14 2022