|
|
A304508
|
|
a(n) = 5*(3*n+1)*(9*n+8)/2 (n>=0).
|
|
2
|
|
|
20, 170, 455, 875, 1430, 2120, 2945, 3905, 5000, 6230, 7595, 9095, 10730, 12500, 14405, 16445, 18620, 20930, 23375, 25955, 28670, 31520, 34505, 37625, 40880, 44270, 47795, 51455, 55250, 59180, 63245, 67445, 71780, 76250, 80855, 85595, 90470, 95480, 100625, 105905, 111320
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
The second Zagreb index of the single-defect 5-gonal nanocone CNC(5,n) (see definition in the Doslic et al. reference, p. 27).
The second Zagreb index of a simple connected graph is the sum of the degree products d(i)d(j) over all edges ij of the graph.
The M-polynomial of CNC(5,n) is M(CNC(5,n); x,y) = 5*x^2*y^2 + 10*n*x^2*y^3 + 5*n*(3*n+1)*x^3*y^3/2.
More generally, the M-polynomial of CNC(k,n) is M(CNC(k,n); x,y) = k*x^2*y^2 + 2*k*n*x^2*y^3 + k*n*(3*n + 1)*x^3*y^3/2.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: 5*(4 + 22*x + x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2.
(End)
|
|
MAPLE
|
seq((1/2)*(5*(3*n+1))*(9*n+8), n = 0 .. 40);
|
|
MATHEMATICA
|
Array[5 (3 # + 1) (9 # + 8)/2 &, 41, 0] (* or *)
LinearRecurrence[{3, -3, 1}, {20, 170, 455}, 41] (* or *)
CoefficientList[Series[5 (4 + 22 x + x^2)/(1 - x)^3, {x, 0, 40}], x] (* Michael De Vlieger, May 14 2018 *)
|
|
PROG
|
(PARI) a(n) = 5*(3*n+1)*(9*n+8)/2; \\ Altug Alkan, May 14 2018
(PARI) Vec(5*(4 + 22*x + x^2) / (1 - x)^3 + O(x^40)) \\ Colin Barker, May 14 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|