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A249333
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Number of regions formed by extending the sides of a regular n-gon.
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1
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7, 9, 16, 19, 29, 33, 46, 51, 67, 73, 92, 99, 121, 129, 154, 163, 191, 201, 232, 243, 277, 289, 326, 339, 379, 393, 436, 451, 497, 513, 562, 579, 631, 649, 704, 723, 781, 801, 862, 883, 947, 969, 1036, 1059, 1129, 1153, 1226, 1251, 1327, 1353, 1432, 1459, 1541, 1569, 1654, 1683, 1771, 1801
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OFFSET
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3,1
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COMMENTS
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a(n) is the number of regions formed by the affine span of all the sides of a regular n-gon.
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LINKS
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FORMULA
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a(n) = (n^2+2)/2, n even, and a(n) = (n^2+n+2)/2, n odd.
a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5). - Colin Barker, Dec 14 2014
G.f.: -x^3*(3*x^4-x^3-7*x^2+2*x+7) / ((x-1)^3*(x+1)^2). - Colin Barker, Dec 14 2014
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MATHEMATICA
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LinearRecurrence[{1, 2, -2, -1, 1}, {7, 9, 16, 19, 29}, 60] (* Harvey P. Dale, Oct 16 2019 *)
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PROG
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(PARI) a(n)=if(n%2, (n^2+n+2)/2, (n^2+2)/2); \\ Joerg Arndt, Dec 04 2014
(PARI) Vec(-x^3*(3*x^4-x^3-7*x^2+2*x+7)/((x-1)^3*(x+1)^2) + O(x^100)) \\ Colin Barker, Dec 14 2014
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CROSSREFS
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a(n) conjecturally is the same as b(n+1) for A075855 (except for b(1), b(2), b(3)).
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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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