|
|
A305062
|
|
a(n) = 96*2^n + 80.
|
|
3
|
|
|
176, 272, 464, 848, 1616, 3152, 6224, 12368, 24656, 49232, 98384, 196688, 393296, 786512, 1572944, 3145808, 6291536, 12582992, 25165904, 50331728, 100663376, 201326672, 402653264, 805306448, 1610612816, 3221225552, 6442451024, 12884901968, 25769803856, 51539607632, 103079215184, 206158430288, 412316860496, 824633720912, 1649267441744
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
a(n) (n>=0) is the first Zagreb index of the dendrimer graph K[n], defined pictorially in the Ghorbani et al. reference (see Figs. 9, 10, and 11).
The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternatively, it is the sum of the degree sums d(i) + d(j) over all edges ij of the graph.
The M-polynomial of K[n] is M(K[n];x,y) = 2*2^n*x*y^3 + 2*(2^n + 2)*x^2*y^2 + (2^4*2^n -4)*x^2*y^3 + 14*x^3*y^3.
|
|
LINKS
|
|
|
FORMULA
|
|
|
MAPLE
|
seq(96*2^n+80, n = 0 .. 40);
|
|
MATHEMATICA
|
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|