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

0,2

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

Table of n, a(n) for n=0..24.

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

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).

Mathematica

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

Crossrefs

Cf. A030186, A052980.

Sequence in context: A116586 A119366 A034574 * A054665 A134963 A026956

Adjacent sequences: A387616 A387617 A387618 * A387620 A387621 A387622

Keyword

nonn,easy

Author

Greg Dresden and Daeheon Shin, Sep 03 2025

Status

approved