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A278127 a(n) = 99*n + 71. 1
71, 170, 269, 368, 467, 566, 665, 764, 863, 962, 1061, 1160, 1259, 1358, 1457, 1556, 1655, 1754, 1853, 1952, 2051, 2150, 2249, 2348, 2447, 2546, 2645, 2744, 2843, 2942, 3041, 3140, 3239, 3338, 3437, 3536, 3635, 3734, 3833, 3932, 4031, 4130, 4229, 4328, 4427, 4526 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
a(n) (n>=1) is the second Zagreb index of the triple-layered naphthalenophane G(n,n,n) having n hexagons in each layer. 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 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).
REFERENCES
Erica Flapan, When Topology Meets Chemistry, Cambridge Univ. Press, Cambridge, 2000.
LINKS
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.
FORMULA
G.f.: (71 + 28*x)/(1 - x)^2.
MAPLE
seq(99*n+71, n = 0..45);
CROSSREFS
Cf. A278126.
Sequence in context: A142277 A063330 A142344 * A044403 A044784 A142488
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Nov 13 2016
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)