A387619 - OEIS

%I #11 Sep 04 2025 10:53:56

%S 1,2,11,51,235,1092,5064,23489,108954,505377,2344171,10873339,

%T 50435526,233943074,1085135139,5033353844,23347000765,108294084141,

%U 502317568673,2329978980834,10807509809918,50130181109907,232526743191648,1078565548781339,5002881075314417

%N Number of ways to tile a 2 X n strip with squares, dominoes, and (straight and bent) trominoes.

%C Compare to A030186 which counts tilings with just squares and dominoes, and to A052980 which counts tilings with just dominos and bent trominos.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,6,7,2,0,-1).

%F a(n) = 3*a(n-1) + 6*a(n-2) + 7*a(n-3) + 2*a(n-4) - a(n-6).

%F G.f.: (1 - x - x^2 - x^3)/(1 - 3*x - 6*x^2 - 7*x^3 - 2*x^4 + x^6).

%t LinearRecurrence[{3, 6, 7, 2, 0, -1}, {1, 2, 11, 51, 235, 1092}, 40]

%Y Cf. A030186, A052980.

%K nonn,easy

%O 0,2

%A _Greg Dresden_ and Daeheon Shin, Sep 03 2025