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A303647 a(n) = ceiling(a(n-1)/(2^(1/3)-1)+1), a(1)=1. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..26.

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)

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 *)

PROG

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

CROSSREFS

Cf. A195350, A301483, A195339.

Sequence in context: A051196 A273454 A094834 * A147504 A217783 A221862

Adjacent sequences:  A303644 A303645 A303646 * A303648 A303649 A303650

KEYWORD

nonn

AUTHOR

Gregory Gerard Wojnar, Apr 27 2018

STATUS

approved

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Last modified April 19 18:37 EDT 2019. Contains 322290 sequences. (Running on oeis4.)