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A323260
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Number of horizontally convex polyoctagons containing n regular polygons (squares or octagons).
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9
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0, 2, 6, 24, 96, 390, 1582, 6422, 26062, 105768, 429228, 1741898, 7068978, 28687370, 116419254, 472453328, 1917312976, 7780851238, 31576298030, 128143125598, 520031215214, 2110393854816, 8564413235420, 34756154117738, 141047636989250, 572400382184434, 2322918728158854, 9426882974883464
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OFFSET
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0,2
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LINKS
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Colin Barker, Table of n, a(n) for n = 0..1000
K. A. Van'kov, V. M. Zhuravlyov, Regular tilings and generating functions, Mat. Pros. Ser. 3, issue 22, 2018 (127-157) [in Russian]. See Table 1, g_n.
Index entries for linear recurrences with constant coefficients, signature (5,-3,-5,7,-1).
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FORMULA
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G.f. = 2*x*(1-x)^3*(1+x)/(1-5*x+3*x^2+5*x^3-7*x^4+x^5).
a(n) = 2*A323261(n).
a(n) = 5*a(n-1) - 3*a(n-2) - 5*a(n-3) + 7*a(n-4) - a(n-5) for n>5. - Colin Barker, Jan 10 2019
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MATHEMATICA
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CoefficientList[Series[2*x*(1-x)^3*(1+x)/(1-5*x+3*x^2+5*x^3-7*x^4+x^5), {x, 0, 27}], x] (* Amiram Eldar, Jan 10 2019 *)
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PROG
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(PARI) concat(0, Vec(2*x*(1 - x)^3*(1 + x) / (1 - 5*x + 3*x^2 + 5*x^3 - 7*x^4 + x^5) + O(x^30))) \\ Colin Barker, Jan 10 2019
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CROSSREFS
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Cf. A323261-A323269.
Sequence in context: A179363 A084509 A334767 * A147915 A147906 A147898
Adjacent sequences: A323257 A323258 A323259 * A323261 A323262 A323263
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Jan 09 2019
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STATUS
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approved
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