

A249333


Number of regions formed by extending the sides of a regular ngon.


1



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

3,1


COMMENTS

a(n) is the number of regions formed by the affine span of all the sides of a regular ngon.


LINKS

Colin Barker, Table of n, a(n) for n = 3..1000
Index entries for linear recurrences with constant coefficients, signature (1,2,2,1,1).


FORMULA

a(n) = (n^2+2)/2, n even, and a(n) = (n^2+n+2)/2, n odd.
a(n) = a(n1)+2*a(n2)2*a(n3)a(n4)+a(n5).  Colin Barker, Dec 14 2014
G.f.: x^3*(3*x^4x^37*x^2+2*x+7) / ((x1)^3*(x+1)^2).  Colin Barker, Dec 14 2014


MATHEMATICA

LinearRecurrence[{1, 2, 2, 1, 1}, {7, 9, 16, 19, 29}, 60] (* Harvey P. Dale, Oct 16 2019 *)


PROG

(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^4x^37*x^2+2*x+7)/((x1)^3*(x+1)^2) + O(x^100)) \\ Colin Barker, Dec 14 2014


CROSSREFS

a(n) conjecturally is the same as b(n+1) for A075855 (except for b(1), b(2), b(3)).
Sequence in context: A158891 A213220 A087680 * A020691 A145830 A195563
Adjacent sequences: A249330 A249331 A249332 * A249334 A249335 A249336


KEYWORD

nonn,easy


AUTHOR

Richard Stanley, Dec 03 2014


STATUS

approved



