A137200 - OEIS

A137200

Number of ways to tile an n X 1 strip with 1 X 1 squares and 2 X 1 dominoes with the restriction that no three consecutive tiles are of the same type.

%I #10 Jun 13 2015 00:52:34

%S 1,1,2,2,4,5,7,9,13,18,25,34,47,65,90,124,171,236,326,450,621,857,

%T 1183,1633,2254,3111,4294,5927,8181,11292,15586,21513,29694,40986,

%U 56572,78085,107779,148765,205337,283422,391201,539966,745303,1028725,1419926,1959892

%N Number of ways to tile an n X 1 strip with 1 X 1 squares and 2 X 1 dominoes with the restriction that no three consecutive tiles are of the same type.

%C Without the restriction one gets the Fibonacci numbers, A000045.

%C Might be called the no-tri-bonacci numbers.

%H Brian Rice, <a href="/A137200/a137200.txt">Proof of the recurrence</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1).

%F a(n) = a(n-1) + a(n-4) for n>4; g.f.: (1+x^2+x^4)/(1-x-x^4). Also a(n) = a(n-2) + a(n-4) + a(n-5).

%e For example (using 1's to denote squares and 2's to denote dominoes), a(6)=7 because you have the tilings 11211, 1122, 1212, 1221, 2112, 2121 and 2211 and no others.

%t Join[{1},LinearRecurrence[{1,0,0,1},{1,2,2,4},50]] (* _Harvey P. Dale_, Jul 26 2011 *)

%Y Cf. A000045.

%K nonn

%O 0,3

%A _Barry Cipra_, Mar 03 2008