A115341 a(n) = abs(A154879(n+1)).

2, 4, 0, 8, 8, 24, 40, 88, 168, 344, 680, 1368, 2728, 5464, 10920, 21848, 43688, 87384, 174760, 349528, 699048, 1398104, 2796200, 5592408, 11184808, 22369624, 44739240, 89478488, 178956968, 357913944, 715827880, 1431655768, 2863311528

Offset: 0

Author

Roger L. Bagula, Mar 06 2006

Keywords

• nonn
• easy
• less

Comments

General form: a(n)=2^n-a(n-1). - Vladimir Joseph Stephan Orlovsky, Dec 11 2008

For n>=1, a(n) is a(n) is the number of generalized compositions of n+3 when there are i^2-2*i-1 different types of i, (i=1,2,...). - Milan Janjic, Sep 24 2010

Links

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

Crossrefs

Cf. A001045, A078008, A097073. - Vladimir Joseph Stephan Orlovsky, Dec 11 2008

Programs

Magma

[2] cat [(2^(n+1)-8*(-1)^n)/3: n in [1..30]]; // G. C. Greubel, Dec 30 2017

Mathematica

g0[n_] = 2 - Sum[(-1)^(i + 1)/Sqrt[2]^(2*i), {i, 0, n}] f[x_] = ZTransform[g0[n], n, x] g[n_] = InverseZTransform[f[1/x], x, n] a0 = Table[Abs[g[n]], {n, 1, 25}]
k=0;lst={k};Do[k=2^n-k;AppendTo[lst, k], {n, 3, 5!}];lst (* Vladimir Joseph Stephan Orlovsky, Dec 11 2008 *)
Table[If[n==0, 2, (2^(n+1)-8*(-1)^n)/3], {n,0,30}] (* G. C. Greubel, Dec 30 2017 *)

PARI

for(n=0,30, print1(if(n==0, 2, (2^(n+1)-8*(-1)^n)/3), ", ")) \\ G. C. Greubel, Dec 30 2017

Formula

a(n) = (2^(n+1)-8*(-1)^n)/3, n>0.

a(n) = a(n-1) + 2*a(n-2), n>2.

G.f.: 2+4*x*(1-x)/((1+x)*(1-2*x)).

Extensions

Edited by the Associate Editors of the OEIS, Aug 21 2009