A356622 Number of ways to tile a hexagonal strip made up of 4*n equilateral triangles, using triangles and diamonds.

1, 5, 39, 317, 2585, 21085, 171987, 1402873, 11443033, 93339173, 761354199, 6210256613, 50656169297, 413195081581, 3370372805763, 27491645850097, 224245398092113, 1829137434684101, 14920010771362215

Offset: 0

Author

Greg Dresden and Aarnav Gogri, Aug 16 2022

Keywords

• nonn
• easy

Comments

Here is the hexagonal strip:

______________ __

/\ /\ /\ /\ / \ /

/\/\/\/\/ ... \/

\ /\ /\ /\ /\ /\

\/\/\/\/\ /\

The two types of tiles are triangles and diamonds (each of which can be rotated). Here are the two types of tiles:

__ __

\ / \ \

\/ and \_\.

Examples

			For n=4, here is one of the a(4)=2585 ways to tile this strip (of 16 triangles) using triangles and diamonds.
    ________________
   /   /\  /\  /   /
  /__ /  \/__\/__ /
  \  /\  /\   \  /\
   \/__\/__\___\/__\
		

Links

• Index entries for linear recurrences with constant coefficients, signature (9,-7,1).

Crossrefs

Bisection of A355327. Cf. A356623.

Programs

Mathematica

LinearRecurrence[{9, -7, 1}, {1, 5, 39}, 40]

Formula

a(n) = A355327(2*n).

a(n) = 9*a(n-1) - 7*a(n-2) + a(n-3).

G.f.: (1 - 4 x + x^2)/(1 - 9 x + 7 x^2 - x^3).