A387619 Number of ways to tile a 2 X n strip with squares, dominoes, and (straight and bent) trominoes.

1, 2, 11, 51, 235, 1092, 5064, 23489, 108954, 505377, 2344171, 10873339, 50435526, 233943074, 1085135139, 5033353844, 23347000765, 108294084141, 502317568673, 2329978980834, 10807509809918, 50130181109907, 232526743191648, 1078565548781339, 5002881075314417

Offset: 0

Author

Greg Dresden and Daeheon Shin, Sep 03 2025

Keywords

• nonn
• easy
• new

Comments

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

Links

• Index entries for linear recurrences with constant coefficients, signature (3,6,7,2,0,-1).

Crossrefs

Cf. A030186, A052980.

Programs

Mathematica

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

Formula

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

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