cp's OEIS Frontend

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 A137200 #10 Jun 13 2015 00:52:34
%S A137200 1,1,2,2,4,5,7,9,13,18,25,34,47,65,90,124,171,236,326,450,621,857,
%T A137200 1183,1633,2254,3111,4294,5927,8181,11292,15586,21513,29694,40986,
%U A137200 56572,78085,107779,148765,205337,283422,391201,539966,745303,1028725,1419926,1959892
%N 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.
%C A137200 Without the restriction one gets the Fibonacci numbers, A000045.
%C A137200 Might be called the no-tri-bonacci numbers.
%H A137200 Brian Rice, <a href="/A137200/a137200.txt">Proof of the recurrence</a>
%H A137200 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1).
%F A137200 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 A137200 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 A137200 Join[{1},LinearRecurrence[{1,0,0,1},{1,2,2,4},50]] (* _Harvey P. Dale_, Jul 26 2011 *)
%Y A137200 Cf. A000045.
%K A137200 nonn
%O A137200 0,3
%A A137200 _Barry Cipra_, Mar 03 2008