



0, 0, 0, 1, 1, 3, 3, 7, 6, 13, 10, 21, 15, 31, 21, 43, 28, 57, 36, 73, 45, 91, 55, 111, 66, 133, 78, 157, 91, 183, 105, 211, 120, 241, 136, 273, 153, 307, 171, 343, 190, 381, 210, 421, 231, 463, 253, 507, 276, 553, 300, 601
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OFFSET

3,6


COMMENTS

a(n) is the number of the distinct symmetric 6gon in a regular ngon where vertices of 6gon are placed on vertices of ngon. See illustration.


LINKS

Table of n, a(n) for n=3..54.
Kival Ngaokrajang, Illustration of initial terms
Index entries for linear recurrences with constant coefficients, signature (0,3,0,3,0,1).


FORMULA

a(3) = a(4) = a(5) = 0; for n >= 6, a(n) = (n/22)^2(n/22)+1 if even n, a(n) = (n/25/2)*(n/25/2+1)/2 if odd n.
From Colin Barker, Aug 19 2014: (Start)
a(n) = (71+41*(1)^n4*(7+3*(1)^n)*n+(3+(1)^n)*n^2)/16 for n>4.
a(n) = 3*a(n2)3*a(n4)+a(n6) for n>10.
G.f.: x^6*(x^4+x+1) / ((x1)^3*(x+1)^3).
(End)


PROG

(PARI)a(n) = if(n<6, 0, if(Mod(n, 2)==0, (n/22)^2(n/22)+1, (n/25/2)*(n/25/2+1)/2))
for (n=3, 100, print1(a(n), ", "))
(PARI) concat([0, 0, 0], Vec(x^6*(x^4+x+1)/((x1)^3*(x+1)^3) + O(x^100))) \\ Colin Barker, Aug 19 2014


CROSSREFS

Cf. A001399: 3gon in ngon, A226088: 4gon in ngon, A004526: symmetric 4gon in ngon, A008805: symmetric 5gon in ngon.
Sequence in context: A096273 A069981 A000199 * A324877 A201932 A161771
Adjacent sequences: A243096 A243097 A243098 * A243100 A243101 A243102


KEYWORD

nonn,easy


AUTHOR

Kival Ngaokrajang, Aug 19 2014


STATUS

approved



