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 A296193 Numerators of Harary index for the n-Mycielski graph. 0
 0, 1, 15, 75, 162, 1317, 2610, 20505, 40212, 315957, 622350, 4917585, 9739512, 77326797, 153754290, 1224577065, 2440906812, 19477524837, 38880209430, 310591650945, 620507282112, 4959998206077, 9913902403770, 79274639451225, 158494393505412, 1267625772746517 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Denominators are 1, 1, 2, followed by 2, 1, 2, 1, .... LINKS Eric Weisstein's World of Mathematics, Harary Index Eric Weisstein's World of Mathematics, Mycielski Graph Index entries for linear recurrences with constant coefficients, signature (0, 30, 0, -273, 0, 820, 0, -576). FORMULA a(n) = ((3 + (-1)^n)*(432 - 135*2^(n + 2) + 112*3^n + 81*4^n))/1152 for n > 3. a(n) = 30*a(n-2) - 273*a(n-4) + 820*a(n-6) - 576*a(n-8) for n > 11. G.f.: x^2*(1 + 15*x + 45*x^2 - 288*x^3 - 660*x^4 + 1845*x^5 + 650*x^6 -    6162*x^7 - 576*x^8 + 4320*x^9)/(1 - 30*x^2 + 273*x^4 - 820*x^6 + 576*x^8). EXAMPLE 0, 1, 15/2, 75/2, 162, 1317/2, 2610, 20505/2, 40212, ... MATHEMATICA Table[If[n == 1, 0, 3/4 - 15 2^(-4 + n) + (7 3^(-2 + n))/4 + 9 4^(-3 + n)], {n, 30}] // Numerator Join[{0, 1, 15}, Table[((3 + (-1)^n) (432 - 135 2^(n + 2) + 112 3^n + 81 4^n))/1152, {n, 4, 20}]] Join[{0, 1, 15}, LinearRecurrence[{0, 30, 0, -273, 0, 820, 0, -576}, {75, 162, 1317, 2610, 20505, 40212, 315957, 622350}, 20]] CoefficientList[Series[x (1 + 15 x + 45 x^2 - 288 x^3 - 660 x^4 + 1845 x^5 + 650 x^6 - 6162 x^7 - 576 x^8 + 4320 x^9)/(1 - 30 x^2 + 273 x^4 - 820 x^6 + 576 x^8), {x, 0, 20}], x] PROG (PARI) first(n) = Vec(x^2*(1 + 15*x + 45*x^2 - 288*x^3 - 660*x^4 + 1845*x^5 + 650*x^6 - 6162*x^7 - 576*x^8 + 4320*x^9)/(1 - 30*x^2 + 273*x^4 - 820*x^6 + 576*x^8) + O(x^(n+1)), -n) \\ Iain Fox, Dec 07 2017 CROSSREFS Sequence in context: A214453 A317657 A339518 * A135916 A211812 A266395 Adjacent sequences:  A296190 A296191 A296192 * A296194 A296195 A296196 KEYWORD nonn AUTHOR Eric W. Weisstein, Dec 07 2017 STATUS approved

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Last modified November 26 21:07 EST 2021. Contains 349344 sequences. (Running on oeis4.)