A164096 -id:A164096 - cp's OEIS frontend

A164095 a(n) = 2*a(n-2) for n > 2; a(1) = 5, a(2) = 6.

5, 6, 10, 12, 20, 24, 40, 48, 80, 96, 160, 192, 320, 384, 640, 768, 1280, 1536, 2560, 3072, 5120, 6144, 10240, 12288, 20480, 24576, 40960, 49152, 81920, 98304, 163840, 196608, 327680, 393216, 655360, 786432, 1310720, 1572864, 2621440, 3145728

Offset: 1

Klaus Brockhaus, Aug 10 2009

nonn

Interleaving of A020714 and A007283 without initial term 3.
Partial sums are in A164096.
Binomial transform is A048655 without initial 1, second binomial transform is A161941 without initial 2, third binomial transform is A164037, fourth binomial transform is A161731 without initial 1, fifth binomial transform is A164038, sixth binomial transform is A164110.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0, 2).

Cf. A020714 (5*2^n), A007283 (3*2^n), A164096, A048655, A161941, A164037, A161731, A164038, A164110, A070876.

[ n le 2 select n+4 else 2*Self(n-2): n in [1..40] ];

LinearRecurrence[{0,2},{5,6},50] (* or *) With[{nn=20},Riffle[NestList[ 2#&,5,nn],NestList[2#&,6,nn]]] (* Harvey P. Dale, Aug 15 2020 *)

a(n) = A070876(n)/3.
a(n) = (4-(-1)^n)*2^(1/4*(2*n-1+(-1)^n)).
G.f.: x*(5+6*x)/(1-2*x^2).

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

Original entry on oeis.org

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)

cp's OEIS Frontend

A164095 a(n) = 2*a(n-2) for n > 2; a(1) = 5, a(2) = 6.

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