A301483 a(n) = floor(a(n-1)/(2^(1/3)-1)) with a(1)=1.

1, 3, 11, 42, 161, 619, 2381, 9160, 35241, 135583, 521631, 2006882, 7721121, 29705639, 114287161, 439699520, 1691665681, 6508382763, 25039844851, 96336348522, 370636962881, 1425959779059, 5486126574341, 21106896023080, 81205027571321, 312421897357543

Offset: 1

Author

Gregory Gerard Wojnar, Mar 22 2018

Keywords

• nonn

Comments

a(n+1)/a(n) approaches 1/(2^(1/3)-1).

Crossrefs

Cf. A024537, A195350 (also has 1/(2^(1/3)-1) ratio), A303647.

Programs

Magma

[n le 1 select 1 else Floor(Self(n-1)/(2^(1/3)-1)): n in [1..30]]; // Vincenzo Librandi, Apr 04 2018

Maple

a:=proc(n) option remember;
   if n<1 then 0  else if n=1 then 1 else floor(a(n-1)/(2^(1/3)-1))
end if end if end proc:
seq(a(n), n=1..25);

Mathematica

RecurrenceTable[{a[1]==1, a[n]==Floor[a[n-1]/(2^(1/3)-1)]}, a, {n, 30}] (* Vincenzo Librandi, Apr 04 2018 *)

PARI

a=vector(50); a[1]=1; for(n=2, #a, a[n]=a[n-1]\(2^(1/3)-1)); a \\ Altug Alkan, Mar 22 2018

Formula

Conjectures from Colin Barker, Apr 01 2018: (Start)

G.f.: x*(1 - x - x^2) / ((1 - x)*(1 - 3*x - 3*x^2 - x^3)).

a(n) = 4*a(n-1) - 2*a(n-3) - a(n-4) for n>4.

(End)

a(n) = A195350(n) + A303647(n-2) - A195339(n-4) (conjectured).