A305166 a(n) = 164*2^n - 140.

24, 188, 516, 1172, 2484, 5108, 10356, 20852, 41844, 83828, 167796, 335732, 671604, 1343348, 2686836, 5373812, 10747764, 21495668, 42991476, 85983092, 171966324, 343932788, 687865716, 1375731572, 2751463284, 5502926708, 11005853556, 22011707252, 44023414644, 88046829428, 176093658996, 352187318132

Offset

0,1

Comments

a(n) is the second Zagreb index of the second type dendrimer nanostar NS2[n], defined pictorially in the Chen et al. reference (Fig. 1).

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 M-polynomial of NS2[n] is M(NS2[n]; x, y) = 2*(4*2^n-1)*x^2*y^2 + 16*(2*n - 1)*x^2*y^3 + 4*(2^n - 1)*x^3*y^3 (n>=0).

Links

Table of n, a(n) for n=0..31.

S. Chen and J. Yang, Second-order and third-order connectivity indices of dendrimer nanostars, International Mathematical Forum, 6, No, 5, 2011, 223-228.

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

Index entries for linear recurrences with constant coefficients, signature (3,-2).

Formula

From Vincenzo Librandi, May 28 2018: (Start)

G.f.: 4*(6 + 29*x)/((1 - 2*x)*(1 - x)).

a(n) = 3*a(n-1) - 2*a(n-2). (End)

Maple

seq(164*2^n-140, n = 0 .. 40);

Mathematica

Table[164 2^n - 140, {n, 0, 33}] (* Vincenzo Librandi, May 28 2018 *)

Prog

(Magma) [164*2^n-140: n in [0..33]]; // Vincenzo Librandi, May 28 2018

Crossrefs

Cf. A305163, A305164, A305165.

Sequence in context: A052758 A241434 A143040 * A128960 A047057 A066406

Adjacent sequences: A305163 A305164 A305165 * A305167 A305168 A305169

Keyword

nonn,easy

Author

Emeric Deutsch, May 27 2018

Status

approved