

A277108


a(n) = 4n*(n+5).


1



24, 56, 96, 144, 200, 264, 336, 416, 504, 600, 704, 816, 936, 1064, 1200, 1344, 1496, 1656, 1824, 2000, 2184, 2376, 2576, 2784, 3000, 3224, 3456, 3696, 3944, 4200, 4464, 4736, 5016, 5304, 5600, 5904, 6216, 6536, 6864, 7200
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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 Mpolynomial 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 nwheel 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, Mpolynomial and degreebased topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93102.
Eric Weisstein's World of Mathematics, Helm Graph
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

G.f.: G(z) = 8z(32z)/(1z)^3.
a(n) = 4*A028557(n) = 8*A055998(n).


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

Cf. A028557, A055998, A132761.
Sequence in context: A216697 A332541 A316361 * A039375 A043198 A043978
Adjacent sequences: A277105 A277106 A277107 * A277109 A277110 A277111


KEYWORD

nonn,easy


AUTHOR

Emeric Deutsch, Nov 05 2016


STATUS

approved



