OFFSET
1,1
COMMENTS
a(n) is the second Zagreb index of the helm graph H[n] (n>=3).
The second Zagreb index of a simple connected graph g is the sum of the degree products d(i)d(j) over all edges ij of g.
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. - Emeric Deutsch, May 11 2018
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. - Emeric Deutsch, May 11 2018
a(n) - 16*n + 1 is a square. - Muniru A Asiru, Jun 01 2018
LINKS
Muniru A Asiru, Table of n, a(n) for n = 1..5000
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
Eric Weisstein's World of Mathematics, Helm Graph
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
MAPLE
seq(4*n^2+20*n, n = 1 .. 40);
MATHEMATICA
Table[4 n (n + 5), {n, 40}] (* or *)
Rest@ CoefficientList[Series[8 x (3 - 2 x)/(1 - x)^3, {x, 0, 40}], x] (* Michael De Vlieger, Nov 06 2016 *)
PROG
(PARI) a(n)=4*n*(n+5) \\ Charles R Greathouse IV, Jun 17 2017
(GAP) List([1..50], n->4*n*(n+5)); # Muniru A Asiru, Jun 01 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Nov 05 2016
STATUS
approved