%I #17 Jan 01 2023 19:43:41
%S 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,
%T 56,49,64,56,72,64,81,72,90,81,100,90,110,100,121,110,132,121,144,132,
%U 156,144,169,156,182,169,196,182,210,196,225,210,240,225,256,240,272,256
%N Numerators of special continued fraction for 2*zeta(3).
%D Y. V. Nesterenko, A few remarks on zeta(3), Mathematical Notes, 59 (No. 6, 1996), 625-636.
%H Y. V. Nesterenko, <a href="http://www.ufr-mi.u-bordeaux.fr/~brisebar/GT/9899/Nest/nest29avril.html">Zeta(3) and recurrence relations.</a>
%H Yu. V. Nesterenko, <a href="http://dx.doi.org/10.1007/BF02307212">A few remarks on zeta(3)</a>, Math. Notes 59 (1996) 625-636. [From _R. J. Mathar_, Jul 31 2010]
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,1,-1,-1,1).
%F a(n) = A008733(n-1), n>2. - _R. J. Mathar_, Jul 31 2010
%p 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
%t 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 *)
%Y Cf. A060804, A060806, A060807, A060808, A008733.
%Y Cf. A152648 (2*zeta(3)).
%K nonn,cofr
%O 1,1
%A _N. J. A. Sloane_, Apr 29 2001
%E More terms from _R. J. Mathar_, Jul 31 2010