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A320431 The number of tiles inside a regular n-gon 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,3

COMMENTS

Sequence proposed by Thomas Young: draw the regular n-gon and construct 2*n lines that run from both ends of the n edges perpendicular into the n-gon 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 non-overlapping tiles inside the n-gon with edges that are sections of the lines or n-gon 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^2-1 = A157914(n), n>1. - Thomas Young (tyoung(AT)district16.org), Nov 11 2017

G.f.: x^3 +x^4 -x^5*(31+13*x-22*x^2-14*x^3+7*x^4+5*x^5) / ( (x-1)^3*(1+x)^3 ). - R. J. Mathar, Jan 21 2019

a(n) = 1+n*A064680(n-2), 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

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Last modified April 7 15:56 EDT 2020. Contains 333306 sequences. (Running on oeis4.)