A115098 -id:A115098 - cp's OEIS frontend

A168610 a(n) = 3^n + 5.

6, 8, 14, 32, 86, 248, 734, 2192, 6566, 19688, 59054, 177152, 531446, 1594328, 4782974, 14348912, 43046726, 129140168, 387420494, 1162261472, 3486784406, 10460353208, 31381059614, 94143178832, 282429536486, 847288609448

Offset: 0

Vincenzo Librandi, Dec 01 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-3).

Cf. A168613.

I:=[6, 8]; [n le 2 select I[n] else 4*Self(n-1)-3*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jul 06 2012

CoefficientList[Series[2*(3-8*x)/((1-x)*(1-3*x)),{x,0,40}],x] (* Vincenzo Librandi, Jul 06 2012 *)
LinearRecurrence[{4,-3}, {6, 8}, 25] (* G. C. Greubel, Jul 27 2016 *)

a(n)=3^n+5 \\ Charles R Greathouse IV, Oct 07 2015

a(n) = 3*a(n-1) - 10 with a(0)=6.
G.f.: 2*(3 - 8*x)/((1-x)*(1-3*x)). - Vincenzo Librandi, Jul 06 2012
a(n) = 4*a(n-1) -3*a(n-2). - Vincenzo Librandi, Jul 06 2012
a(n) = 2*A115098(n)+2. - Bruno Berselli, Jul 06 2012
E.g.f.: exp(3*x) + 5*exp(x). - G. C. Greubel, Jul 27 2016

Formula and examples edited to use correct offset by Jon E. Schoenfield, Jun 19 2010

A178674 a(n) = 3^n + 3.

Original entry on oeis.org

4, 6, 12, 30, 84, 246, 732, 2190, 6564, 19686, 59052, 177150, 531444, 1594326, 4782972, 14348910, 43046724, 129140166, 387420492, 1162261470, 3486784404, 10460353206, 31381059612, 94143178830, 282429536484, 847288609446, 2541865828332, 7625597484990, 22876792454964

Offset: 0

Vincenzo Librandi, Dec 25 2010

a(n) is the deficiency of 3^n * 5. - Patrick J. McNab, May 27 2017

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-3).

Cf. A034472, A115098, A168607, A168609, A168610.

List([0..40], n -> 3^n+3); # G. C. Greubel, Jan 27 2019

Magma
```
[3^n+3: n in [0..35]];
```

Table[3^n+3, {n, 0, 40}] (* or *) CoefficientList[Series[(4-10x)/((1-x) (1-3x)), {x, 0, 30}], x] (* Vincenzo Librandi, May 13 2014 *)

a(n)=3^n+3 \\ Charles R Greathouse IV, Oct 07 2015

[3^n+3 for n in range(40)] # G. C. Greubel, Jan 27 2019

a(n) = 3*(a(n-1) - 2), a(0)=4.
From R. J. Mathar, Jan 05 2011: (Start)
G.f.: (4-10*x)/((1-3*x)*(1-x)).
a(n) = 2*A115098(n). (End)
a(n) = 4*a(n-1) - 3*a(n-2) for n > 1. - Vincenzo Librandi, May 13 2014
E.g.f.: exp(x)*(exp(2*x) + 3). - Elmo R. Oliveira, Apr 02 2025

A387435 Number of dominating sets in the n-Dorogovtsev-Goltsev-Mendes graph.

Original entry on oeis.org

3, 7, 45, 13293, 461504710485, 37306936154345310416554765472710125

Offset: 0

Eric W. Weisstein, Aug 29 2025

a(6) has 104 decimal digits. - Andrew Howroyd, Aug 31 2025

Andrew Howroyd, Table of n, a(n) for n = 0..8
Eric Weisstein's World of Mathematics, Dominating Set.
Eric Weisstein's World of Mathematics, Dorogovtsev-Goltsev-Mendes Graph.

Cf. A115098 (domination number), A368456.

Join[{3}, Map[{1, 2, 1} . # &, NestList[Function[{p2, q1, q2}, {p2 (p2^2 + q1^2), q1^2 (q2 + p2), q2 (q1^2 + q2^2)}] @@ # &, {1, 2, 2}, 7]]] (* Eric W. Weisstein, Sep 03 2025 *)

step(v)={my([p2,q1,q2]=v); [p2*(p2^2+q1^2), q1^2*(q2+p2), q2*(q1^2+q2^2)]}
a(n)={if(n==0, 3, my(v=[1,2,2]); for(i=2, n, v=step(v)); v[1]+2*v[2]+v[3])} \\ Andrew Howroyd, Aug 31 2025

a(4) onwards from Andrew Howroyd, Aug 29 2025

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A168610 a(n) = 3^n + 5.

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A178674 a(n) = 3^n + 3.

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A387435 Number of dominating sets in the n-Dorogovtsev-Goltsev-Mendes graph.

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