A292055 Wiener index of the n-Mycielski graph.

0, 1, 15, 90, 435, 1926, 8175, 33930, 139035, 565326, 2287335, 9224370, 37116435, 149110326, 598350495, 2399080410, 9613258635, 38503648926, 154166045655, 617117746050, 2469830101635, 9883394613126, 39545794780815, 158219815525290, 632989146141435

Offset

1,3

Links

Table of n, a(n) for n=1..25.

Eric Weisstein's World of Mathematics, Mycielski Graph

Eric Weisstein's World of Mathematics, Wiener Index

Index entries for linear recurrences with constant coefficients, signature (10,-35,50,-24).

Formula

a(n) = (216 - 27*2^(n + 3) - 56*3^n + 81*4^n)/144 for n > 1.

a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4).

G.f.: x^2*(1 + 5*x - 25*x^2 + 10*x^3)/(1 - 10*x + 35*x^2 - 50*x^3 + 24*x^4).

Mathematica

Table[If[n == 1, 0, (216 - 27 2^(n + 3) - 56 3^n + 81 4^n)/144], {n,
  30}]
Join[{0}, LinearRecurrence[{10, -35, 50, -24}, {1, 15, 90, 435}, 20]]
CoefficientList[Series[x (1 + 5 x - 25 x^2 + 10 x^3)/(1 - 10 x + 35 x^2 - 50 x^3 + 24 x^4), {x, 0, 20}], x]

Crossrefs

Sequence in context: A328994 A001297 A005716 * A263628 A263629 A320524

Adjacent sequences: A292052 A292053 A292054 * A292056 A292057 A292058

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 08 2017

Status

approved