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A261064
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a(n) = (3^n-1)*(n+1)/4.
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5
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1, 6, 26, 100, 363, 1274, 4372, 14760, 49205, 162382, 531438, 1727180, 5580127, 17936130, 57395624, 182948560, 581130729, 1840247318, 5811307330, 18305618100, 57531942611, 180441092746, 564859072956, 1765184603000, 5507375961373, 17157594341214
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OFFSET
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1,2
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COMMENTS
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Number of non-selfintersecting broken lines in a convex (n+1)-gon. (National Math Contest "Atanas Radev" 2020, Bulgaria) - Ivaylo Kortezov, Jan 18 2020
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LINKS
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National Math Contest "Atanas Radev", Problems and Solutions, problem 8.4 ("Задача 8.4" in Bulgarian), Jan 2020.
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FORMULA
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G.f.: -x*(-1 + 2*x) / ( (3*x - 1)^2*(x - 1)^2 ).
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MATHEMATICA
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LinearRecurrence[{8, -22, 24, -9}, {1, 6, 26, 100}, 30] (* Vincenzo Librandi, Aug 31 2016 *)
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PROG
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(PARI) first(m)=vector(m, i, (3^i-1)*(i+1)/4); /* Anders Hellström, Aug 08 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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STATUS
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approved
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