A304518 -id:A304518 - cp's OEIS frontend

A304517 a(n) = 16*2^n - 11 (n>=1).

21, 53, 117, 245, 501, 1013, 2037, 4085, 8181, 16373, 32757, 65525, 131061, 262133, 524277, 1048565, 2097141, 4194293, 8388597, 16777205, 33554421, 67108853, 134217717, 268435445, 536870901, 1073741813, 2147483637, 4294967285, 8589934581, 17179869173, 34359738357, 68719476725, 137438953461, 274877906933, 549755813877

Offset: 1

Emeric Deutsch, May 15 2018

a(n) is the number of edges of the nanostar dendrimer NS2[n] from the Madanshekaf et al. reference.

Colin Barker, Table of n, a(n) for n = 1..1000
A. Madanshekaf and M. Moradi, The first geometric-arithmetic index of some nanostar dendrimers, Iranian J. Math. Chemistry, 5, Supplement 1, 2014, s1-s6.
Index entries for linear recurrences with constant coefficients, signature (3,-2).

Cf. A304518, A304518.

First bisection of A164096 without 5. First column of the table in A224701.

List([1..40],n->16*2^n-11); # Muniru A Asiru, May 15 2018

Maple
```
seq(16*2^n-11, n = 1 .. 40);
```

Rest@ CoefficientList[Series[x (21 - 10 x)/((1 - x) (1 - 2 x)), {x, 0, 35}], x] (* or *)
LinearRecurrence[{3, -2}, {21, 53}, 35] (* or *)
Array[16*2^# - 11 &, 35] (* Michael De Vlieger, May 15 2018 *)

Vec(x*(21 - 10*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 15 2018

From Colin Barker, May 15 2018: (Start)
G.f.: x*(21 - 10*x) / ((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
(End)

A304519 a(n) = 72*2^n -56 (n>=1).

Original entry on oeis.org

88, 232, 520, 1096, 2248, 4552, 9160, 18376, 36808, 73672, 147400, 294856, 589768, 1179592, 2359240, 4718536, 9437128, 18874312, 37748680, 75497416, 150994888, 301989832, 603979720, 1207959496, 2415919048, 4831838152, 9663676360, 19327352776, 38654705608, 77309411272, 154618822600, 309237645256, 618475290568

Offset: 1

Emeric Deutsch, May 15 2018

a(n) is the second Zagreb index of the nanostar dendrimer NS2[n] from the Madanshekaf et al. reference.
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*2^n *x*y^2 + (8*2^n - 5)*x^2*y^2 + (6*2^n - 6)*x^2*y^3.

Colin Barker, Table of n, a(n) for n = 1..1000
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
A. Madanshekaf and M. Moradi, The first geometric-arithmetic index of some nanostar dendrimers, Iranian J. Math. Chemistry, 5, Supplement 1, 2014, s1-s6.
Index entries for linear recurrences with constant coefficients, signature (3,-2).

Cf. A304517, A304518.

List([1..40],n->72*2^n-56); # Muniru A Asiru, May 15 2018

Maple
```
seq(72*2^n-56, n = 1 .. 40);
```

Vec(8*x*(11 - 4*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 15 2018

From Colin Barker, May 15 2018: (Start)
G.f.: 8*x*(11 - 4*x) / ((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
(End)

cp's OEIS Frontend

A304517 a(n) = 16*2^n - 11 (n>=1).

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