

A320431


The number of tiles inside a regular ngon created by lines that run from each of the vertices of the n edges orthogonal to these edges.


2



1, 1, 31, 13, 71, 25, 127, 41, 199, 61, 287, 85, 391, 113, 511, 145, 647, 181, 799, 221, 967, 265, 1151, 313, 1351, 365, 1567, 421, 1799, 481, 2047, 545, 2311, 613, 2591, 685, 2887, 761, 3199, 841, 3527, 925, 3871, 1013, 4231, 1105, 4607, 1201, 4999, 1301, 5407, 1405, 5831, 1513, 6271, 1625, 6727, 1741
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OFFSET

3,3


COMMENTS

Sequence proposed by Thomas Young: draw the regular ngon and construct 2*n lines that run from both ends of the n edges perpendicular into the ngon until they hit an opposite edge. (For n even the lines actually hit another vertex, so there are only n additional lines). a(n) is the number of nonoverlapping tiles inside the ngon with edges that are sections of the lines or ngon edges.


LINKS

Table of n, a(n) for n=3..60.
R. J. Mathar, OEIS A320431
Index to sequences on drawing diagonals in regular polygons
Index entries for linear recurrences with constant coefficients, signature (0,3,0,3,0,1).


FORMULA

a(2n) = 2*n^2+2*n+1 = A001844(n), n>1. a(2n+1) = 8*n^21 = A157914(n), n>1.  Thomas Young (tyoung(AT)district16.org), Nov 11 2017
G.f.: x^3 +x^4 x^5*(31+13*x22*x^214*x^3+7*x^4+5*x^5) / ( (x1)^3*(1+x)^3 ).  R. J. Mathar, Jan 21 2019
a(n) = 1+n*A064680(n2), n>=5.  R. J. Mathar, Jan 21 2019


CROSSREFS

Cf. A165217, A320422
Sequence in context: A178561 A065821 A040934 * A107114 A328204 A077397
Adjacent sequences: A320428 A320429 A320430 * A320432 A320433 A320434


KEYWORD

nonn,easy


AUTHOR

R. J. Mathar, Jan 08 2019


STATUS

approved



