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

Author

N. J. A. Sloane, Apr 29 2001

Keywords

• nonn
• cofr

References

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

Links

• Y. V. Nesterenko, Zeta(3) and recurrence relations.
• Yu. V. Nesterenko, A few remarks on zeta(3), Math. Notes 59 (1996) 625-636. [From _R. J. Mathar_, Jul 31 2010]
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1,1,-1,-1,1).

Crossrefs

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

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

Programs

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 *)

Formula

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

Extensions

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