A089093 - OEIS

%I #12 Mar 24 2018 12:12:35

%S 0,1,4,16,51,154,418,1098,2726,6570,15308,34839,77412,168882,361896,

%T 764097,1590938,3272640,6656426,13403600,26739028,52892435,103806344,

%U 202263470,391460137,752923563,1439737364,2738144031,5181025837

%N Convoluted convolved Fibonacci numbers G_j^(6).

%C The 6th Witt transform of A000045 [Moree]. The 2nd to 5th Witt transforms are (essentially, adding leading zeros) in A089089, A089116, A089117, A089092. [From _R. J. Mathar_, Nov 08 2008]

%H P. Moree, <a href="http://arXiv.org/abs/math.CO/0311205">Convoluted convolved Fibonacci numbers</a>

%H Pieter Moree, <a href="http://dx.doi.org/10.1016/j.disc.2005.03.004">The formal series Witt transform</a>, Discr. Math. no. 295 vol. 1-3 (2005) 143-160.

%F G.f.: (z/6)[1/(1-z-z^2)^6-1/(1-z^2-z^4)^3-1/(1-z^3-z^6)^2+1/(1-z^6-z^12)].

%p with(numtheory): f := z->1/(1-z-z^2): m := proc(r,j) d := divisors(r): W := (1/r)*z*sum(mobius(d[i])*f(z^d[i])^(r/d[i]),i=1..nops(d)): Wser := simplify(series(W,z=0,80)): coeff(Wser,z^j) end: seq(m(6,j),j=1..40);

%t f[k_] = 1/(1 - z^k - z^(2k))^(6/k); (1/6) (f[1] - f[2] - f[3] + f[6]) + O[z]^30 // CoefficientList[#, z]& (* _Jean-François Alcover_, Mar 24 2018 *)

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Dec 05 2003

%E Edited by _Emeric Deutsch_, Mar 06 2004