A352720 a(n) is the number of free polyominoes of width 2 and size n.

1, 1, 4, 5, 12, 18, 37, 60, 117, 200, 379, 669, 1250, 2247, 4168, 7570, 13987, 25549, 47108, 86319, 158978, 291806, 537105, 986786, 1815699, 3337560, 6140047, 11289571, 20767180, 38189927, 70246680, 129191148, 237627757, 437042337, 803861244, 1478488577, 2719392160, 5001663330, 9199544069

Offset

2,3

Links

John Mason, Table of n, a(n) for n = 2..1000

John Mason, Java program

John Mason, Explanation of formulas

R. J. Mathar, Corrigendum to "polyomino enumeration results" (Parkin et al), vixra:1905.0474 (2019) Table 1 column 2.

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

Formula

For a set of recursive formulas to generate a(n), see the link for the Java program extract.

G.f.: x^2*(1 - x^3 - 2*x^4 - x^5 - 2*x^6 - x^7 - x^8)/((1 - x)*(1 + x)*(1 - x - x^2 - x^3)*(1 - x^2 - x^4 - x^6)). - Andrew Howroyd, Nov 06 2025

Example

There is one polyomino, the domino, of width 2 and size 2. So a(2) = 1.
There is one tromino, L-shaped, of width 2. So a(3) = 1.

Crossrefs

Cf. A000105, A335711, A353067.

Sequence in context: A131328 A054451 A309479 * A369697 A308775 A305335

Adjacent sequences: A352717 A352718 A352719 * A352721 A352722 A352723

Keyword

nonn,easy

Author

John Mason, Mar 31 2022

Status

approved