A349842 Expansion of 1/((1 - 2*x)*(1 + x + x^2 + x^3 + x^4)).

1, 1, 2, 4, 8, 17, 33, 66, 132, 264, 529, 1057, 2114, 4228, 8456, 16913, 33825, 67650, 135300, 270600, 541201, 1082401, 2164802, 4329604, 8659208, 17318417, 34636833, 69273666, 138547332, 277094664, 554189329, 1108378657, 2216757314, 4433514628, 8867029256, 17734058513

Offset: 0

Author

Michael A. Allen, Dec 13 2021

Keywords

• nonn
• easy

Comments

Number of ways to tile an n-board (an n X 1 array of 1 X 1 cells) using squares, dominoes, trominoes, tetrominoes, black pentominoes, and white pentominoes.

Row sums of A349841.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,2).

Crossrefs

Row sums of triangles in the same family as A349841: A000079, A001045, A077947, A115451.

Programs

Mathematica

CoefficientList[Series[(1 - x)/((1 - x^5)(1 - 2x)), {x, 0, 35}], x]

Formula

a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + 2*a(n-5) + delta(n,0), a(n<0)=0.

a(n) = 2*a(n-1) + a(n-5) - 2*a(n-6) + delta(n,0) - delta(n,1), a(n<0)=0.

G.f.: 1/(1-x-x^2-x^3-x^4-2*x^5).