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A304385
a(n) = 192*2^n - 31 (n>=1).
2
353, 737, 1505, 3041, 6113, 12257, 24545, 49121, 98273, 196577, 393185, 786401, 1572833, 3145697, 6291425, 12582881, 25165793, 50331617, 100663265, 201326561, 402653153, 805306337, 1610612705, 3221225441, 6442450913, 12884901857, 25769803745, 51539607521
OFFSET
1,1
COMMENTS
a(n) is the second Zagreb index of the molecular graph NS2[n], defined pictorially in the Ashrafi et al. reference (Fig. 2, where NS2[2] is shown).
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 NS2[n] is M(NS2[n]; x,y) = (12*2^n + 2)*x^2*y^2 + (24*2^n - 8)*x^2*y^3 + x^3*y^3.
LINKS
Ali Reza Ashrafi and Parisa Nikzad, Kekulé index and bounds of energy for nanostar dendrimers, Digest J. of Nanomaterials and Biostructures, 4, No. 2, 2009, 383-388.
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 14 2018: (Start)
G.f.: x*(353 - 322*x) / ((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
(End)
MAPLE
seq(192*2^n-31, n = 1 .. 40);
PROG
(GAP) List([1..40], n->192*2^n-31); # Muniru A Asiru, May 13 2018
(PARI) Vec(x*(353 - 322*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 14 2018
CROSSREFS
Cf. A304384.
Sequence in context: A096739 A039664 A054825 * A142565 A265449 A142785
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 13 2018
STATUS
approved