login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A305068 a(n) = 54*n - 18 (n>=1). 2
36, 90, 144, 198, 252, 306, 360, 414, 468, 522, 576, 630, 684, 738, 792, 846, 900, 954, 1008, 1062, 1116, 1170, 1224, 1278, 1332, 1386, 1440, 1494, 1548, 1602, 1656, 1710, 1764, 1818, 1872, 1926, 1980, 2034, 2088, 2142, 2196, 2250, 2304, 2358, 2412, 2466, 2520, 2574, 2628, 2682 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) is the first Zagreb index of the chain silicate network CS(n), defined pictorially in the Javaid et al. reference (Fig. 2, where CS(6) is shown) or in Liu et al. reference (Fig. 4, where CS(8) is shown).

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.

The M-polynomial of CS(n) is M(C(n);x,y) = (n+4)*x^3*y^3 + (4*n - 2)*x^3*y^6 + (n - 2)*x^6*y^6  (n>=2).

LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..5000

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

M. Javaid and C. Y. Jung, M-polynomials and topological indices of silicate and oxide networks, International J. Pure and Applied Math., 115, No. 1, 2017, 129-152.

J.-B. Liu, S. Wang, C. Wang, and S. Hayat, Further results on computation of topological indices of certain networks, IET Control Theory Appl., 11, No. 13, 2017, 2065-2071.

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

FORMULA

From Colin Barker, May 26 2018: (Start)

G.f.: 18*x*(2 + x) / (1 - x)^2.

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

(End)

MAPLE

seq(54*n-18, n = 1..50);

PROG

(PARI) Vec(18*x*(2 + x) / (1 - x)^2 + O(x^50)) \\ Colin Barker, May 26 2018

(GAP) List([1..50], n->54*n-18); # Muniru A Asiru, May 27 2018

CROSSREFS

Cf. A305069.

Sequence in context: A044174 A044555 A283635 * A182467 A060936 A247246

Adjacent sequences:  A305065 A305066 A305067 * A305069 A305070 A305071

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, May 25 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 24 03:39 EST 2020. Contains 338607 sequences. (Running on oeis4.)