A259088 Number of n-celled polyominoes which are of square type.

1, 0, 1, 1, 6, 7, 25, 80, 255, 795, 2919, 10378, 36590, 130716, 480773, 1774714, 6543633, 24208803, 90331307, 339178346, 1277308160, 4819109576

Offset

1,5

Links

Table of n, a(n) for n=1..22.

R. J. Mathar, Corrigendum to "Polynomino enumeration results (Parkin et al, SIAM Fall Meeting 1967)", vixra:1905.0474

T. R. Parkin, L. J. Lander, and D. R. Parkin, Polyomino Enumeration Results, presented at SIAM Fall Meeting, 1967, and accompanying letter from T. J. Lander (annotated scanned copy). See page 21. The 15th entry is not included because their value for A000105(15) was incorrect.

Formula

a(n)+A259087(n) = A000105(n).

Example

a(7) = 25 with 7 free 7-ominoes with a 3x3 hull and 18 with 4x4 hull. a(8) = 80 with 3 free 8-ominoes with a 3x3 hull and 77 with a 4x4 hull. a(9) = 255 with 1 free 9-omino in a 3x3 hull, 181 in a 4x4 hull and 73 in a 5x5 hull. - R. J. Mathar, May 24 2019

Crossrefs

Cf. A259087, A268311, A000105.

Sequence in context: A333550 A219916 A135987 * A200179 A054289 A041078

Adjacent sequences: A259085 A259086 A259087 * A259089 A259090 A259091

Keyword

nonn,more

Author

N. J. A. Sloane, Jun 18 2015

Extensions

a(15)-a(16) from R. J. Mathar, May 22 2019

a(17) from R. J. Mathar, May 27 2019

a(18)-a(22) from John Mason, Nov 19 2021

Status

approved