A278126 a(n) = 78*n + 66.

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

Offset: 0

Author

Emeric Deutsch, Nov 13 2016

Keywords

• nonn
• easy

Comments

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).

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.
• 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).

Crossrefs

Cf. A269100, A278127.

Programs

Maple

seq(78*n+66, n = 0..45);

Mathematica

78*Range[0,50]+66 (* or *) LinearRecurrence[{2,-1},{66,144},50] (* Harvey P. Dale, Jul 27 2025 *)

Formula

G.f.: 6*(11 + 2*x)/(1 - x)^2.

a(n) = 6*A269100(n).