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 A243099 A002061 and A000217 interleaved. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,6 COMMENTS a(n) is the number of the distinct symmetric 6-gon in a regular n-gon where vertices of 6-gon are placed on vertices of n-gon. See illustration. LINKS 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/2-2)^2-(n/2-2)+1 if even n, a(n) = (n/2-5/2)*(n/2-5/2+1)/2 if odd n. From Colin Barker, Aug 19 2014: (Start) a(n) = (71+41*(-1)^n-4*(7+3*(-1)^n)*n+(3+(-1)^n)*n^2)/16 for n>4. a(n) = 3*a(n-2)-3*a(n-4)+a(n-6) for n>10. G.f.: -x^6*(x^4+x+1) / ((x-1)^3*(x+1)^3). (End) PROG (PARI)a(n) = if(n<6, 0, if(Mod(n, 2)==0, (n/2-2)^2-(n/2-2)+1, (n/2-5/2)*(n/2-5/2+1)/2)) for (n=3, 100, print1(a(n), ", ")) (PARI) concat([0, 0, 0], Vec(-x^6*(x^4+x+1)/((x-1)^3*(x+1)^3) + O(x^100))) \\ Colin Barker, Aug 19 2014 CROSSREFS Cf. A001399: 3-gon in n-gon, A226088: 4-gon in n-gon, A004526: symmetric 4-gon in n-gon, A008805: symmetric 5-gon in n-gon. 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

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Last modified December 7 09:33 EST 2019. Contains 329843 sequences. (Running on oeis4.)