A277987 a(n) = 100*n - 28.

-28, 72, 172, 272, 372, 472, 572, 672, 772, 872, 972, 1072, 1172, 1272, 1372, 1472, 1572, 1672, 1772, 1872, 1972, 2072, 2172, 2272, 2372, 2472, 2572, 2672, 2772, 2872, 2972, 3072, 3172, 3272, 3372, 3472, 3572, 3672, 3772, 3872, 3972

Offset: 0

Author

Emeric Deutsch, Nov 12 2016

Keywords

• sign
• easy

Comments

For n>=1, a(n) is the second Zagreb index of the tetrameric 1,3-adamantane TA[n]. 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 the tetrameric 1,3-adamantane can be viewed in the G. H. Fath-Tabar et al. reference.

The M-polynomial of the tetrameric 1,3-adamantane TA[n] is M(TA[n],x,y) = 6*(n+1)*x^2*y^3 + 6*(n-1)*x^2*y^4 + (n-1)*x^4*y^4.

Links

• E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
• G. H. Fath-Tabar, A. Azad, and N. Elahinezhad, Some topological indices of tetrameric 1,3-adamantane, Iranian J. Math. Chemistry, 1, No. 1, 2010, 111-118.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A277986.

Programs

Magma

[100*n-28: n in [0..40]]; // Vincenzo Librandi, Nov 13 2016

Maple

seq(100*n-28, n = 0..40);

Mathematica

100*Range[0,40]-28 (* or *) LinearRecurrence[{2,-1},{-28,72},50] (* Harvey P. Dale, Feb 13 2018 *)

PARI

a(n) = 100*n - 28 \\ Felix Fröhlich, Nov 12 2016

Formula

G.f.: 4*(32*x - 7)/(1 - x)^2.

a(n) = A017293(10*n-3) for n > 0. - Felix Fröhlich, Nov 12 2016

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Nov 13 2016