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A305153 a(n) = 30*2^n + 12. 2
42, 72, 132, 252, 492, 972, 1932, 3852, 7692, 15372, 30732, 61452, 122892, 245772, 491532, 983052, 1966092, 3932172, 7864332, 15728652, 31457292, 62914572, 125829132, 251658252, 503316492, 1006632972, 2013265932, 4026531852, 8053063692, 16106127372, 32212254732, 64424509452, 128849018892, 257698037772 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
a(n) is the first Zagreb index of the dendrimer D[n], defined pictorially in Fig. 1 of the Heydari et al. 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 D[n] is M(D[n];x,y) = 3*2^n*x*y^3 + 6*x^2*y^3 + 3*(2^n - 1)*x^3*y^3 (n>=0).
LINKS
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
A. Heydari and I. Gutman, On the terminal Wiener index of thorn graphs, Kragujevac J. Sci., 32, 2010, 57-64.
FORMULA
From Colin Barker, May 29 2018: (Start)
G.f.: 6*(7 - 9*x) / ((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1) - 2*a(n-2) for n>1.
(End)
MAPLE
seq(30*2^n+12, n = 0..40);
PROG
(PARI) Vec(6*(7 - 9*x) / ((1 - x)*(1 - 2*x)) + O(x^50)) \\ Colin Barker, May 29 2018
CROSSREFS
Cf. A305154.
Sequence in context: A248430 A340384 A330893 * A340570 A261621 A043689
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 27 2018
STATUS
approved

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Last modified February 24 18:59 EST 2024. Contains 370307 sequences. (Running on oeis4.)