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 A320604 Chromatic number of the n-polygon diagonal intersection graph. 0
 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Extended to a(1)-a(2) using the formula/recurrence. LINKS Eric Weisstein's World of Mathematics, Chromatic Number Eric Weisstein's World of Mathematics, Polygon Diagonal Intersection Graph Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 1). FORMULA a(n) = (10 - (-1)^n + cos(n*Pi/3) - cos(2*n*Pi/3))/3. a(n) = a(n-6). G.f.: -x^3*(3 + 3*x + 4*x^2 + 3*x^3 + 4*x^4 + 3*x^5)/((-1 + x)*(1 + x)*(1 - x + x^2)*(1 + x + x^2)). E.g.f.: (1/6)*exp(-x)*(-2-18*exp(x)+20*exp(2*x)+exp((1+(-1)^(1/3))*x)-exp((1+(-1)^(2/3))*x)-exp(x-(-1)^(1/3)*x)+exp(x-(-1)^(2/3)*x)). - Stefano Spezia, Oct 17 2018 MATHEMATICA Table[(10 - (-1)^n + Cos[n Pi/3] - Cos[2 n Pi/3])/3, {n, 20}] Table[Piecewise[{{4, Mod[n, 6] == 1 || Mod[n, 6] == 5}}, 3], {n, 20}] LinearRecurrence[{0, 0, 0, 0, 0, 1}, {4, 3, 3, 3, 4, 3}, 20] CoefficientList[Series[-((3 + 3 x + 4 x^2 + 3 x^3 + 4 x^4 + 3 x^5)/((-1 + x) (1 + x) (1 - x + x^2) (1 + x + x^2))), {x, 0, 20}], x] Simplify[CoefficientList[Series[1/6 E^-x (-2 - 18 E^x + 20 E^(2 x) + E^((1 + (-1)^(1/3)) x) - E^((1 + (-1)^(2/3)) x) - E^(x - (-1)^(1/3) x) + E^(x - (-1)^(2/3) x))/x, {x, 0, 50}], x]*Table[(k+1)!, {k, 0, 50}]] (* Stefano Spezia, Oct 17 2018 *) CROSSREFS Sequence in context: A085415 A187470 A059124 * A282445 A281705 A026858 Adjacent sequences:  A320601 A320602 A320603 * A320605 A320606 A320607 KEYWORD nonn AUTHOR Eric W. Weisstein, Oct 17 2018 STATUS approved

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Last modified April 20 06:31 EDT 2021. Contains 343121 sequences. (Running on oeis4.)