A089110 - OEIS

%I #16 Mar 28 2018 13:07:17

%S 5,11,17,25,38,54,70,89,115,145,175,209,252,300,348,401,465,535,605,

%T 681,770,866,962,1065,1183,1309,1435,1569,1720,1880,2040,2209,2397,

%U 2595,2793,3001,3230,3470,3710,3961,4235,4521,4807,5105,5428,5764,6100,6449

%N Sign twisted convoluted convolved Fibonacci numbers H_5^(r).

%H P. Moree, <a href="https://arxiv.org/abs/math/0311205">Convoluted convolved Fibonacci numbers</a>, arXiv:math/0311205 [math.CO], 2003.

%H Pieter Moree, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL7/Moree/moree12.html">Convoluted Convolved Fibonacci Numbers</a>, Journal of Integer Sequences, Vol. 7 (2004), Article 04.2.2.

%F Empirical g.f.: -x*(x^7-4*x^6+8*x^5-12*x^4+15*x^3-13*x^2+9*x-5) / ((x-1)^4*(x^2+1)^2). - _Colin Barker_, Jul 31 2013

%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((-1)^r*m(r,5),r=1..60);

%t f[z_] = -1/(1 - z - z^2);

%t m[r_, j_] := (1/r)*z*DivisorSum[r, MoebiusMu[#]*f[z^#]^(r/#)&] // SeriesCoefficient[#, {z, 0, j}]&;

%t Table[(-1)^r*m[r, 5], {r, 1, 60}] (* _Jean-François Alcover_, Mar 27 2018 *)

%K nonn

%O 1,1

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

%E Edited by _Emeric Deutsch_, Mar 06 2004