OFFSET
0,1
COMMENTS
For n>0, a(n) is the number of edges in the dendrimer nanostar NS1[n] defined pictorially in the Ashrafi et al. reference (Ns1[3] is shown in Fig. 1) or in the Ahmadi et al. reference (Fig. 1).
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
M. B. Ahmadi and M. Sadeghimehr, Atom bond connectivity index of an infinite class NS1[n] of dendrimer nanostars, Optoelectronics and Advanced Materials, 4(7):1040-1042 July 2010.
Ali Reza Ashrafi and Parisa Nikzad, Kekulé index and bounds of energy for nanostar dendrimers, Digest J. of Nanomaterials and Biostructures, 4, No. 2, 2009, 383-388.
Index entries for linear recurrences with constant coefficients, signature (3,-2).
FORMULA
From Colin Barker, May 18 2018: (Start)
G.f.: (22 - 17*x) / ((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1) - 2*a(n-2) for n>1.
(End)
MAPLE
seq(27*2^n-5, n = 0 .. 40);
MATHEMATICA
27*2^Range[0, 40]-5 (* or *) LinearRecurrence[{3, -2}, {22, 49}, 40] (* Harvey P. Dale, Jan 12 2019 *)
PROG
(PARI) a(n) = 27*2^n - 5; \\ Altug Alkan, May 13 2018
(PARI) Vec((22 - 17*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 18 2018
(GAP) List([1..40], n->27*2^n-5); # Muniru A Asiru, May 13 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 13 2018
EXTENSIONS
Offset changed by N. J. A. Sloane, May 13 2018
STATUS
approved