A303647 a(n) = ceiling(a(n-1)/(2^(1/3)-1)+1), a(1)=1.

1, 5, 21, 82, 317, 1221, 4699, 18080, 69561, 267625, 1029641, 3961362, 15240637, 58635641, 225590199, 867918160, 3339160721, 12846826845, 49425880861, 190157283842, 731596320957, 2814686695261, 10829006332499, 41662675404240, 160289731905481, 616686228261665

Offset: 1

Author

Gregory Gerard Wojnar, Apr 27 2018

Keywords

• nonn

Crossrefs

Cf. A195350, A301483, A195339.

Programs

Maple

a := proc(n) option remember;
       if n<1 then 0 else
       if n=1 then 1 else ceil(a(n-1)/(2^(1/3)-1)+1)
     end if end if end proc;
seq(a(n), n=0..10);

Mathematica

Nest[Append[#, Ceiling[#[[-1]]/(2^(1/3) - 1) + 1]] &, {1}, 25] (* or *)
Rest@ CoefficientList[Series[x (1 + x + x^2)/((1 - x) (1 - 3 x - 3 x^2 - x^3)), {x, 0, 25}], x] (* Michael De Vlieger, Apr 28 2018 *)

PARI

a(n) = if (n==1, 1, ceil(a(n-1)/(2^(1/3)-1)+1)); \\ Michel Marcus, Apr 28 2018

Formula

a(n) = A301483(n+2) - A195350(n+2) + A195339(n-2) (conjectured).

Conjectures from Colin Barker, Apr 28 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)