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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

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.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

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

Adjacent sequences: A278124 A278125 A278126 * A278128 A278129 A278130

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Nov 13 2016

STATUS

approved

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Last modified December 5 21:40 EST 2022. Contains 358594 sequences. (Running on oeis4.)