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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
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
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Dec 07 2017
STATUS
approved