OFFSET
0,2
COMMENTS
Compare g.f. to the Lambert series of A028594:
1 + 4*Sum_{n>=1} Chi(n,7)*n*x^n/(1-x^n).
Here Chi(n,7) = principal Dirichlet character of n modulo 7.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
EXAMPLE
G.f.: A(x) = 1 + 4*x + 24*x^2 + 80*x^3 + 336*x^4 + 696*x^5 + 3360*x^6 +...
where A(x) = 1 + 1*4*x + 2*12*x^2 + 5*16*x^3 + 12*28*x^4 + 29*24*x^5 + 70*48*x^6 + 169*4*x^7 + 408*60*x^8 + 985*52*x^9 +...+ Pell(n)*A028594(n)*x^n +...
The g.f. is also given by the identity:
A(x) = 1 + 4*( 1*1*x/(1-2*x-x^2) + 2*2*x^2/(1-6*x^2+x^4) + 5*3*x^3/(1-14*x^3-x^6) + 12*4*x^4/(1-34*x^4+x^8) + 29*5*x^5/(1-82*x^5-x^10) + 70*6*x^6/(1-198*x^6+x^12) + 0*169*7*x^7/(1+478*x^7-x^14) +...).
The values of the Dirichlet character Chi(n,7) repeat [1,1,1,1,1,1,0, ...].
MATHEMATICA
A028594[n_]:= If[n < 1, Boole[n == 0], 4*Sum[If[Mod[d, 7] > 0, d, 0], {d, Divisors@n}]]; Join[{1}, Table[Fibonacci[n, 2]*A028594[n], {n, 1, 50}]] (* G. C. Greubel, Jan 03 2018 *)
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 10 2012
STATUS
approved