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A304614
a(n) = 420*2^n - 222.
4
198, 618, 1458, 3138, 6498, 13218, 26658, 53538, 107298, 214818, 429858, 859938, 1720098, 3440418, 6881058, 13762338, 27524898, 55050018, 110100258, 220200738, 440401698, 880803618, 1761607458, 3523215138, 7046430498, 14092861218, 28185722658, 56371445538, 112742891298
OFFSET
0,1
COMMENTS
a(n) is the first Zagreb index of the nanostar dendrimer NS[n] from the Mirzargar reference.
The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternatively, it is the sum of the degree sums d(i) + d(j) over all edges ij of the graph.
The M-polynomial of NS[n] is M(NS[n];x,y) = (30*2^n - 12)*x^2*y^2 + (42*2^n - 24)*x^2*y^3 + (15*2^n - 9)*x^3*y^3.
LINKS
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
M. Mirzargar, PI, Szeged and edge Szeged polynomials of a dendrimer nanostar, MATCH, Commun. Math. Comput. Chem. 62, 2009, 363-370.
FORMULA
From Colin Barker, May 17 2018: (Start)
G.f.: 6*(33 + 4*x) / ((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1) - 2*a(n-2) for n>1.
(End)
MAPLE
seq(420*2^n-222, n = 0 .. 40);
MATHEMATICA
420*2^Range[0, 30]-222 (* or *) LinearRecurrence[{3, -2}, {198, 618}, 30] (* Harvey P. Dale, Feb 07 2023 *)
PROG
(GAP) List([0..40], n->420*2^n-222); # Muniru A Asiru, May 17 2018
(PARI) a(n) = 420*2^n - 222; \\ Altug Alkan, May 17 2018
(PARI) Vec(6*(33 + 4*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 17 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 16 2018
STATUS
approved