|
|
A132761
|
|
a(n) = n*(n+17).
|
|
19
|
|
|
0, 18, 38, 60, 84, 110, 138, 168, 200, 234, 270, 308, 348, 390, 434, 480, 528, 578, 630, 684, 740, 798, 858, 920, 984, 1050, 1118, 1188, 1260, 1334, 1410, 1488, 1568, 1650, 1734, 1820, 1908, 1998, 2090, 2184, 2280, 2378, 2478, 2580, 2684, 2790, 2898, 3008, 3120
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
a(n) is the first Zagreb index of the helm graph H[n] (n>=3). - Emeric Deutsch, Nov 05 2016
a(n) is the first Zagreb index of the graph obtained by joining one vertex of the cycle graph C[n] with each vertex of a second cycle graph C[n].
The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternately, it is the sum of the degree sums d(i)+d(j) over all edges ij of the graph. (End)
The M-polynomial of the Helm graph H[n] is M(H[n];x,y) = n*x*y^4 + n*x^4*y^4 + n*x^4*y^n.
The helm graph H[n] is the graph obtained from an n-wheel graph by adjoining a pendant edge at each node of the cycle. (End)
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Helm Graph.
|
|
FORMULA
|
a(n) = n*(n + 17).
Sum_{n>=1} 1/a(n) = H(17)/17 = A001008(17)/A102928(17) = 42142223/208288080, where H(k) is the k-th harmonic number.
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/17 - 1768477/41657616. (End)
|
|
MATHEMATICA
|
Table[n(n+17), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 18, 38}, 50] (* Harvey P. Dale, Sep 12 2020 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|