A238411 -id:A238411 - cp's OEIS frontend

A242371 Modified eccentric connectivity index of the cycle graph with n vertices, C[n].

12, 32, 40, 72, 84, 128, 144, 200, 220, 288, 312, 392, 420, 512, 544, 648, 684, 800, 840, 968, 1012, 1152, 1200, 1352, 1404, 1568, 1624, 1800, 1860, 2048, 2112, 2312, 2380, 2592, 2664, 2888, 2964, 3200, 3280, 3528, 3612, 3872, 3960, 4232, 4324, 4608, 4704

Offset: 3

Nilanjan De, Jun 08 2014

nonn

The modified eccentric connectivity index of a graph is defined as the sum of the products of eccentricity with the total degree of neighboring vertices, over all vertices of the graph. This is a generalization of eccentric connectivity index.

a(n) = 4*A093353(n-1) = n*A168273(n) for n>2. - Alois P. Heinz, Jun 26 2014

			a(3) = 3*4 = 12 because there are 3 vertices and each vertex has eccentricity 1 and the total degree of neighboring vertices is 4.

Nilanjan De, Table of n, a(n) for n = 3..100
N. De, S. M. A. Nayeem and A. Pal, Bounds for modified eccentric connectivity index, Advanced Modeling and Optimization, 16(1) (2014) 133-142.
N. De, S. M. A. Nayeem and A. Pal, Bounds for modified eccentric connectivity index, arXiv:1402.1870 [math.CO], 2014.
Eric Weisstein's World of Mathematics, Graph Eccentricity

Cf. A093353, A168273, A206490, A238410, A238411.

a:= n-> n*(2*n-1+(-1)^n):
seq(a(n), n=3..60);  # Alois P. Heinz, Jun 26 2014

a[n_] := 2n(n-Boole[OddQ[n]]);
Table[a[n], {n, 3, 50}] (* Jean-François Alcover, Nov 28 2018 *)

a(n) = if (n % 2, 2*n*(n-1), 2*n^2); \\ Michel Marcus, Jun 20 2014

a(n) = 2*n*(n-1) if n is odd; and a(n) = 2*n^2 if n is even (n>2).

G.f.: -4*x^3*(3+5*x-4*x^2-2*x^3+2*x^4)/((x+1)^2*(x-1)^3). - Alois P. Heinz, Jun 26 2014

A269265 a(0) = a(1) = 1; thereafter a(n) = a(n-1) + a(n-2) if n is even, otherwise a(n) = a(n-1)^2.

Original entry on oeis.org

1, 1, 2, 4, 6, 36, 42, 1764, 1806, 3261636, 3263442, 10650053687364, 10650056950806, 113423713055411194304049636, 113423713055421844361000442, 12864938683278671740537145884937248491231415124195364, 12864938683278671740537145998360961546653259485195806

Offset: 0

Vincenzo Librandi, Feb 23 2016

nonn

The first bisection is A007018, the second bisection is A174864 (with an only initial 1).

After 2, all terms belong to A238411.

Cf. A007018, A174864, A238411.

[n le 2 select 1 else IsEven(n) select Self(n-1)^2 else Self(n-1)+Self(n-2): n in [1..20]];

a[n_] := If[OddQ@n, a[n - 1] + a[n - 2], a[n - 1]^2]; a[0] = 1; Array[a, 17]

a(n) = ( 1 + Sum_{k=0..floor(n/2)-1} a(2*k+1) )^(3-(-1)^n)/2 for n>1.

Edited and extended by Bruno Berselli, Feb 25 2016

cp's OEIS Frontend

A242371 Modified eccentric connectivity index of the cycle graph with n vertices, C[n].

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