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A304608
a(n) = 288*2^n + 178 (n >= 1).
4
754, 1330, 2482, 4786, 9394, 18610, 37042, 73906, 147634, 295090, 590002, 1179826, 2359474, 4718770, 9437362, 18874546, 37748914, 75497650, 150995122, 301990066, 603979954, 1207959730, 2415919282, 4831838386, 9663676594, 19327353010, 38654705842, 77309411506, 154618822834, 309237645490, 618475290802
OFFSET
1,1
COMMENTS
a(n) is the second Zagreb index of the nanostar dendrimer G[n] from the Ashrafi et al. reference.
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 G[n] is M(G[n]; x,y) = 4*x*y^4 + (18*2^n + 21)*x^2*y^2 + (36*2^n - 9)*x^2*y^3 + 3*x^2*y^4 + 9*x^3*y^4.
LINKS
A. R. Ashrafi, A. Karbasioun, and M. V. Diudea, Computing Wiener and detour indices of a new type of nanostar dendrimers, MATCH Commun. Math. Comput. Chem. 65, 2011, 193-200.
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
FORMULA
From Michael De Vlieger, May 16 2018: (Start)
G.f.: 2*x*(377 - 466*x)/(1 - 3*x + 2*x^2).
a(n) = 3*a(n - 1) - 2*a(n - 2) for n > 2. (End)
MAPLE
seq(288*2^n+178, n = 1 .. 40);
MATHEMATICA
CoefficientList[Series[2 (377 - 466 x)/(1 - 3 x + 2 x^2), {x, 0, 30}], x] (* or *)
LinearRecurrence[{3, -2}, {754, 1330}, 31] (* or *)
Array[288*2^# + 178 &, 31] (* Michael De Vlieger, May 16 2018 *)
PROG
(PARI) a(n) = 288*2^n + 178; \\ Altug Alkan, May 15 2018
(PARI) Vec(2*x*(377 - 466*x)/(1 - 3*x + 2*x^2) + O(x^40)) \\ Colin Barker, May 23 2018
(GAP) List([1..40], n->288*2^n+178); # Muniru A Asiru, May 16 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 15 2018
STATUS
approved