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A278126
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a(n) = 78*n + 66.
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1
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66, 144, 222, 300, 378, 456, 534, 612, 690, 768, 846, 924, 1002, 1080, 1158, 1236, 1314, 1392, 1470, 1548, 1626, 1704, 1782, 1860, 1938, 2016, 2094, 2172, 2250, 2328, 2406, 2484, 2562, 2640, 2718, 2796, 2874, 2952, 3030, 3108, 3186, 3264, 3342, 3420, 3498, 3576
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OFFSET
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0,1
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COMMENTS
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a(n) (n>=1) is the first Zagreb index of the triple-layered naphthalenophane G(n,n,n) having n hexagons in each layer. 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 G(p,q,r) can be viewed in the E. Flapan references.
The M-polynomial of the triple layered naphthalenophane G(p,q,r) is M(G(p,q,r),x,y) = 8*x^2*y^2 + 4*(p + q + r + 2)*x^2*y^3 + (p + q + r - 1)*x^3*y^3 (p, q, r>=1).
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REFERENCES
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Erica Flapan, When Topology Meets Chemistry, Cambridge Univ. Press, Cambridge, 2000.
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LINKS
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Table of n, a(n) for n=0..45.
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
Erica Flapan and Brian Forcum, Intrinsic chirality of triple-layered naphthalenophane and related graphs, J. Math. Chemistry, 24, 1998, 379-388.
I. Gutman and K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50, 2004, 83-92.
Index entries for linear recurrences with constant coefficients, signature (2,-1).
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FORMULA
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G.f.: 6*(11 + 2*x)/(1 - x)^2.
a(n) = 6*A269100(n).
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MAPLE
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seq(78*n+66, n = 0..45);
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CROSSREFS
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Cf. A269100, A278127.
Sequence in context: A206030 A174929 A072430 * A044317 A044698 A122125
Adjacent sequences: A278123 A278124 A278125 * A278127 A278128 A278129
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KEYWORD
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nonn,easy
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AUTHOR
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Emeric Deutsch, Nov 13 2016
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STATUS
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approved
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