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
R. J. Mathar, OEIS A320431
Thomas Young, R. J. Mathar, The surfer and the hut: a polygon dissection (2019)
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
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Jan 08 2019
STATUS
approved