A305157 a(n) = 164*2^n - 99.

65, 229, 557, 1213, 2525, 5149, 10397, 20893, 41885, 83869, 167837, 335773, 671645, 1343389, 2686877, 5373853, 10747805, 21495709, 42991517, 85983133, 171966365, 343932829, 687865757, 1375731613, 2751463325, 5502926749, 11005853597, 22011707293, 44023414685, 88046829469, 176093659037

Offset

0,1

Comments

a(n) (n>=0) is the second Zagreb index of the nanostar dendrimer G(n), defined pictorially in the Darafsheh et al. reference (see Fig. 1, where G(2) is shown).

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 G(n) is M(G(n);x,y) = 8*2^n*x^2*y^2 + (16*2^n - 12)*x^2*y^3 + (4*2^n - 3)*x^3*y^3.

References

M. R. Darafsheh, M. H. Khalifeh, Calculation of the Wiener, Szeged, and PI indices of a certain nanostar dendrimer, Ars Comb., 100, 2011, 289-298.

Links

Muniru A Asiru, Table of n, a(n) for n = 0..700

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 Colin Barker, May 30 2018: (Start)

G.f.: (65 + 34*x) / ((1 - x)*(1 - 2*x)).

a(n) = 3*a(n-1) - 2*a(n-2) for n>1.

(End)

Maple

seq(164*2^n-99, n = 0 .. 40);

Prog

(GAP) List([0..40], n->164*2^n-99); # Muniru A Asiru, May 30 2018
(PARI) Vec((65 + 34*x) / ((1 - x)*(1 - 2*x)) + O(x^30)) \\ Colin Barker, May 30 2018

Crossrefs

Cf. A226264, A305155, A305156.

Sequence in context: A056777 A048512 A237039 * A038637 A158686 A115342

Adjacent sequences: A305154 A305155 A305156 * A305158 A305159 A305160

Keyword

nonn,easy

Author

Emeric Deutsch, May 28 2018

Status

approved