A060805 Numerators of special continued fraction for 2*zeta(3).

2, 1, 2, 1, 4, 2, 6, 4, 9, 6, 12, 9, 16, 12, 20, 16, 25, 20, 30, 25, 36, 30, 42, 36, 49, 42, 56, 49, 64, 56, 72, 64, 81, 72, 90, 81, 100, 90, 110, 100, 121, 110, 132, 121, 144, 132, 156, 144, 169, 156, 182, 169, 196, 182, 210, 196, 225, 210, 240, 225, 256, 240, 272, 256

Offset

1,1

References

Y. V. Nesterenko, A few remarks on zeta(3), Mathematical Notes, 59 (No. 6, 1996), 625-636.

Links

Table of n, a(n) for n=1..64.

Y. V. Nesterenko, Zeta(3) and recurrence relations.

Yu. V. Nesterenko, A few remarks on zeta(3), Math. Notes 59 (1996) 625-636.

Index entries for linear recurrences with constant coefficients, signature (1,1,-1,1,-1,-1,1).

Formula

a(n) = A008733(n-1), n>2. - R. J. Mathar, Jul 31 2010

G.f.: x*(2 - x - x^2 + 2*x^6 - x^8)/(1 - x - x^2 + x^3 - x^4 + x^5 + x^6 - x^7). - Charles R Greathouse IV, May 25 2026

Maple

A060805 := proc(n) local nshf, k ; if n <= 2 then op(n, [2, 1]) ; else nshf := n-1 ; k := floor(nshf/4) ; if nshf mod 4 = 1 then k*(k+1) ; elif nshf mod 4 = 0 then (k+1)^2 ; elif nshf mod 4 = 2 then (k+1)*(k+2) ; else (k+1)^2 ; end if; end if; end proc: seq(A060805(n), n=1..80) ; # R. J. Mathar, Jul 31 2010

Mathematica

Join[{2, 1}, LinearRecurrence[{1, 1, -1, 1, -1, -1, 1}, {2, 1, 4, 2, 6, 4, 9}, 100]] (* Jean-François Alcover, Apr 01 2020 *)

Prog

(PARI) a(n)=if(n>2, my(q=n\4); q^2+[0, 2*q+1, q, 3*q+2][n%4+1], 3-n) \\ Charles R Greathouse IV, May 25 2026

Crossrefs

Cf. A060804, A060806, A060807, A060808, A008733.

Cf. A152648 (2*zeta(3)).

Sequence in context: A338201 A029173 A002331 * A184342 A030767 A352933

Adjacent sequences: A060802 A060803 A060804 * A060806 A060807 A060808

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane, Apr 29 2001

Extensions

More terms from R. J. Mathar, Jul 31 2010

Status

approved