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%I #23 Jul 16 2015 15:32:03
%S 1,3,11,44,186,810,3582,15952,71242,318441,1423411,6360809,28415254,
%T 126900911,566604462,2529439891,11290673434,50394458326,224918228462,
%U 1003813933351,4479953995624,19993503244811,89228022987483,398209768217607
%N Number of Level 2 hexagonal polyominoes with cheesy blocks and n cells.
%C 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.
%H Ray Chandler, <a href="/A167012/b167012.txt">Table of n, a(n) for n = 1..100</a>
%H Svjetlan Feretic, <a href="http://arxiv.org/abs/0910.4780">Polyominoes with nearly convex columns: A model with semidirected blocks</a>, Math. Commun. 15 (2010), 77--97, arXiv:0910.4780v1 [math.CO].
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Polyhex_(mathematics)">Polyhex</a>
%H <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (16, -107, 391, -850, 1108, -797, 169, 266, -317, -159, 913, -1081, 672, -446, 268, -7, 158, -404, 222, -42, 70, -34).
%F G.f.: (x*(1 - 13*x + 70*x^2 - 202*x^3 + 336*x^4 - 317*x^5 + 143*x^6 + 18*x^7 - 84*x^8 + 11*x^9 + 227*x^10 - 375*x^11 + 267*x^12 - 165*x^13 + 134*x^14 - 21*x^15 + 4*x^16 - 124*x^17 + 98*x^18 - 12*x^19 + 28*x^20 - 16*x^21)) / (1 - 16*x + 107*x^2 - 391*x^3 + 850*x^4 - 1108*x^5 + 797*x^6 - 169*x^7 - 266*x^8 + 317*x^9 + 159*x^10 - 913*x^11 + 1081*x^12 - 672*x^13 + 446*x^14 - 268*x^15 + 7*x^16 - 158*x^17 + 404*x^18 - 222*x^19 + 42*x^20 - 70*x^21 + 34*x^22).
%t LinearRecurrence[{16,-107,391,-850,1108,-797,169,266,-317,-159,913,-1081,672,-446,268,-7,158,-404,222,-42,70,-34},{1,3,11,44,186,810,3582,15952,71242,318441,1423411,6360809,28415254,126900911,566604462,2529439891,11290673434,50394458326,224918228462,1003813933351,4479953995624,19993503244811},24] (* _Ray Chandler_, Jul 16 2015 *)
%Y Cf. A059716, A167011, A167013.
%K nonn,easy
%O 1,2
%A _Jonathan Vos Post_, Oct 26 2009
%E Edited by _Ralf Stephan_, Feb 07 2014
%E Extended by _Ray Chandler_, Jul 16 2015
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