A167011 Number of Level 1 hexagonal polyominoes with cheesy blocks and n cells.

1, 3, 11, 44, 184, 784, 3363, 14451, 62097, 266716, 1145074, 4914448, 21087401, 90472315, 388129627, 1665025084, 7142592112, 30639836360, 131436162099, 563822359859, 2418629133001, 10375190596724, 44506436288882, 190919170388912, 818985577308225, 3513200788519075

Offset: 1

Author

Jonathan Vos Post, Oct 26 2009

Keywords

• nonn
• easy

Comments

From Table 1, p.24, of Feretic. By level 0 cheesy polyominoes, and so too by level 0 polyominoes with cheesy blocks, Feretic appears to mean the usual column-convex polyominoes (A059716). See the paper for his definition.

Links

• Svjetlan Feretic, Polyominoes with nearly convex columns: A model with semidirected blocks, Math. Commun. 15 (2010), 77--97, arXiv:0910.4780v1 [math.CO].
• Wikipedia, Polyhex
• Index entries for linear recurrences with constant coefficients, signature (9,-27,32,-13,3,1).

Crossrefs

Cf. A059716, A167012, A167013.

Programs

Mathematica

LinearRecurrence[{9,-27,32,-13,3,1},{1,3,11,44,184,784},26] (* Ray Chandler, Jul 16 2015 *)
Rest[CoefficientList[Series[x*(-1+6x-11x^2+6x^3-2x^4)/(-1+9x-27x^2+32x^3-13x^4+3x^5+x^6),{x,0,26}],x]] (* Ray Chandler, Jul 16 2015 *)

Formula

G.f.: x(-1+6x-11x^2+6x^3-2x^4)/(-1+9x-27x^2+32x^3-13x^4+3x^5+x^6).

Extensions

Edited by Ralf Stephan, Feb 07 2014