A304828 a(n) = 344*7^n/21 - 128/3 (n>=1).

72, 760, 5576, 39288, 275272, 1927160, 13490376, 94432888, 661030472, 4627213560, 32390495176, 226733466488, 1587134265672, 11109939859960, 77769579019976, 544387053140088, 3810709371980872, 26674965603866360, 186724759227064776, 1307073314589453688, 9149513202126176072

Offset

1,1

Comments

a(n) is the first Zagreb index of the crystal structure cubic carbon CCC(n), defined in the Baig et al. and in the Gao et al. references.

The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternatively, it is the sum of the degree sums d(i) + d(j) over all edges ij of the graph.

For n>=2 the M-polynomial of the crystal structure cubic carbon CCC(n) is M(CCC(n); x,y) = 72*7^(n-2)*x^3*y^3 + 24*7^(n-2)*x^3*y^4 + (76*7^(n-2) - 16)*x^4*y^4/3.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

A. Q. Baig, M. Imran, W. Khalid, and M. Naeem, Molecular description of carbon graphite and crystal cubic carbon structures, Canadian J. Chem., 95, 674-686, 2017.

E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.

W. Gao, M. K. Siddiqui, M. Naeem and N. A. Rehman, Topological characterization of carbon graphite and crystal cubic carbon structures, Molecules, 22, 1496, 1-12, 2017.

Index entries for linear recurrences with constant coefficients, signature (8,-7).

Formula

From Colin Barker, May 21 2018: (Start)

G.f.: 8*x*(9 + 23*x) / ((1 - x)*(1 - 7*x)).

a(n) = 8*a(n-1) - 7*a(n-2) for n>2. (End)

Maple

seq((344*7^(n-1)-128)*(1/3), n = 1 .. 25);

Mathematica

LinearRecurrence[{8, -7}, {72, 760}, 30] (* Harvey P. Dale, Aug 24 2019 *)

Prog

(PARI) Vec(8*x*(9 + 23*x) / ((1 - x)*(1 - 7*x)) + O(x^30)) \\ Colin Barker, May 21 2018

Crossrefs

Cf. A304826, A304827, A304829.

Sequence in context: A253917 A008448 A282213 * A268780 A086579 A113855

Adjacent sequences: A304825 A304826 A304827 * A304829 A304830 A304831

Keyword

nonn,easy

Author

Emeric Deutsch, May 21 2018

Status

approved