A189003 Number of domino tilings of the 5 X n grid with upper left corner removed iff n is odd.

1, 1, 8, 15, 95, 192, 1183, 2415, 14824, 30305, 185921, 380160, 2332097, 4768673, 29253160, 59817135, 366944287, 750331584, 4602858719, 9411975375, 57737128904, 118061508289, 724240365697, 1480934568960, 9084693297025, 18576479568193, 113956161827912

Offset: 0

Author

Alois P. Heinz, Apr 15 2011

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..550
• Index entries for sequences related to dominoes
• Index entries for linear recurrences with constant coefficients, signature (0,15,0,-32,0,15,0,-1).

Crossrefs

5th row of array A189006.

Bisections give: A003775 (even part), A006238 (odd part).

Programs

Maple

a:= n-> (<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <-1|15|-32|15>>^iquo(n, 2, 'r').
        `if`(r=0, <<8, 1, 1, 8>>, <<1, 0, 1, 15>>))[3, 1]:
seq(a(n), n=0..30);

Mathematica

a[n_] := Product[2(2+Cos[2 j Pi/(n+1)]+Cos[k Pi/3]), {k, 1, 2}, {j, 1, n/2} ] // Round;
Table[a[n], {n, 0, 24}] (* Jean-François Alcover, Aug 19 2018, after A099390 *)

Formula

G.f.: (x-1)*(1+x)*(x^4+x^3-6*x^2+x+1) / (-x^8+15*x^6-32*x^4+15*x^2-1).