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A167012
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Number of Level 2 hexagonal polyominoes with cheesy blocks and n cells.
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3
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1, 3, 11, 44, 186, 810, 3582, 15952, 71242, 318441, 1423411, 6360809, 28415254, 126900911, 566604462, 2529439891, 11290673434, 50394458326, 224918228462, 1003813933351, 4479953995624, 19993503244811, 89228022987483, 398209768217607
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (16, -107, 391, -850, 1108, -797, 169, 266, -317, -159, 913, -1081, 672, -446, 268, -7, 158, -404, 222, -42, 70, -34).
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FORMULA
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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).
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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