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A304831 a(n) = 123*2^n - 135. 1
111, 357, 849, 1833, 3801, 7737, 15609, 31353, 62841, 125817, 251769, 503673, 1007481, 2015097, 4030329, 8060793, 16121721, 32243577, 64487289, 128974713, 257949561, 515899257, 1031798649, 2063597433, 4127195001, 8254390137, 16508780409, 33017560953, 66035122041, 132070244217, 264140488569, 528280977273 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
a(n) is the second Zagreb index of the dendrimer molecule D[n], defined in 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 the dendrimer molecule D[n] is M(D[n]; x,y) = 6*2^n*x^2*y^2 + 6(2*2^n - 3)*x^2*y^3 + 3*(2^n - 1)*x^3*y^3.
LINKS
A. R. Ashrafi, H. Shabani, M. V. Diudea, Balaban index of dendrimers, MATCH, Commun. Math. Comput. Chem. 69, 2013, 151-158.
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
FORMULA
From Colin Barker, May 20 2018: (Start)
G.f.: 3*x*(37 + 8*x) / ((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
(End)
MAPLE
seq(123*2^n - 135, n = 1 .. 35);
PROG
(GAP) List([1..40], n->123*2^n-135); # Muniru A Asiru, May 19 2018
(PARI) Vec(3*x*(37 + 8*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 20 2018
CROSSREFS
Cf. A304830.
Sequence in context: A244857 A225329 A277960 * A364023 A304516 A259246
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 19 2018
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)