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A278122 a(n) = 204*2^n - 248. 1
160, 568, 1384, 3016, 6280, 12808, 25864, 51976, 104200, 208648, 417544, 835336, 1670920, 3342088, 6684424, 13369096, 26738440, 53477128, 106954504, 213909256, 427818760, 855637768, 1711275784, 3422551816, 6845103880, 13690208008, 27380416264, 54760832776 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
a(n) is the first Zagreb index of the nanostar dendrimer NSC5C6[n].
The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternately, it is the sum of the degree sums d(i)+d(j) over all edges ij of the graph. The pictorial definition of NSC5C6[n] can be viewed in the A. R. Ashrafi et al. and in the M. Rostami et al. references.
The M-polynomial of the nanostar dendrimer NSC5C6[n] is M(NSC5C6[n],x,y) = (4*2^n - 6)*x*y^3 + 4*2^n*x*y^4 + (4*2^n -6)*x^2*y^2 + (18*2^n - 28)*x^2*y^3 + 2*2^n*x^2*y^4 + (7*2^n - 10)*x^3*y^3 + 2^n*x^4*y^4.
LINKS
A. R. Ashrafi and P. Nikzad, Szeged index of nanostar dendrimers, Digest J. of Nanomaterials and Biostructures, 4, No. 1, 2009, 155-157.
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
I. Gutman and K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50, 2004, 83-92.
M. Rostami, M. Shabanian, and H. Moghanian, Some topological indices for theoretical study of two types of nanostar dendrimers, Digest J. of Nanomaterials and Biostructures, 7, 1, 2012, 247-252.
FORMULA
G.f.: 8*x*(20 + 11*x)/((1 - x)*(1 - 2*x)).
MAPLE
seq(204*2^n-248, n = 1..35);
PROG
(Magma) [204*2^n-248: n in [1..35]]; // Vincenzo Librandi, Nov 13 2016
(PARI) a(n)=204*2^n-248 \\ Charles R Greathouse IV, Nov 13 2016
CROSSREFS
Cf. A278123.
Sequence in context: A133530 A278129 A184070 * A233917 A233910 A234658
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Nov 12 2016
STATUS
approved

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Last modified May 26 21:09 EDT 2024. Contains 372844 sequences. (Running on oeis4.)