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A335711 The number of free polyominoes of width 2 and height n. 2
2, 6, 12, 30, 65, 158, 362, 875, 2064, 4984, 11914, 28764, 69155, 166956, 402372, 971413, 2343518, 5657754, 13654968 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

The second column of A268371.

LINKS

Table of n, a(n) for n=2..20.

Index entries for sequences related to polyominoes

FORMULA

Conjecture: a(n) = A107769(n-1) + A005409(floor((n+3)/2)).

Conjectures from Colin Barker, Jun 24 2020: (Start)

G.f.: x^2*(2 - 8*x^2 + 2*x^3 - x^4 + x^5 + x^6) / ((1 - x)*(1 - 2*x - x^2)*(1 - 2*x^2 - x^4)).

a(n) = 3*a(n-1) + a(n-2) - 7*a(n-3) + 3*a(n-4) - a(n-5) + a(n-6) + a(n-7) for n>8.

(End)

EXAMPLE

a(2)=2, bounding box 2 X 2, counts the L-shaped 3-omino and the full block 4-omino.

a(3)=6, bounding box 2 X 3, counts three 4-ominoes, two 5-omioes, and the full 2 X 3 block 6-omino.

a(4)=12, bounding box 2 X 4, counts three 5-ominoes, six 6-ominoes, two 7-ominoes, and the full 2 X 4 block 8-omino.

CROSSREFS

Cf. A268371, A107769 (asymmetric), A005409 (C_2 symmetry and higher).

Sequence in context: A283477 A182863 A161507 * A032177 A095349 A291518

Adjacent sequences:  A335708 A335709 A335710 * A335712 A335713 A335714

KEYWORD

nonn,more

AUTHOR

R. J. Mathar, Jun 18 2020

EXTENSIONS

a(12)-a(20) from Jean-Luc Manguin, Jun 23 2020

STATUS

approved

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Last modified September 26 20:34 EDT 2021. Contains 347672 sequences. (Running on oeis4.)