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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

Table of n, a(n) for n=1..26.

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.)