A296193 Numerators of Harary index for the n-Mycielski graph.

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

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