The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A204060 G.f.: Sum_{n>=1} Fibonacci(n^2)*x^(n^2). 4
 1, 0, 0, 3, 0, 0, 0, 0, 34, 0, 0, 0, 0, 0, 0, 987, 0, 0, 0, 0, 0, 0, 0, 0, 75025, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14930352, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7778742049, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10610209857723, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 37889062373143906 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Compare g.f. to the Lambert series identity: Sum_{n>=1} lambda(n)*x^n/(1-x^n) = Sum_{n>=1} x^(n^2). Liouville's function lambda(n) = (-1)^k, where k is number of primes dividing n (counted with multiplicity). LINKS FORMULA G.f.: Sum_{n>=1} lambda(n)*Fibonacci(n)*x^n/(1 - Lucas(n)*x^n + (-1)^n*x^(2*n)), where lambda(n) = A008836(n) and Lucas(n) = A000204(n). EXAMPLE G.f.: A(x) = x + 3*x^4 + 34*x^9 + 987*x^16 + 75025*x^25 + 14930352*x^36 +... where A(x) = x/(1-x-x^2) + (-1)*1*x^2/(1-3*x^2+x^4) + (-1)*2*x^3/(1-4*x^3-x^6) + (+1)*3*x^4/(1-7*x^4+x^8) + (-1)*5*x^5/(1-11*x^5-x^10) + (+1)*8*x^6/(1-18*x^6+x^12) +...+ lambda(n)*fibonacci(n)*x^n/(1 - Lucas(n)*x^n + (-1)^n*x^(2*n)) +... PROG (PARI) {a(n)=issquare(n)*fibonacci(n)} (PARI) {lambda(n)=local(F=factor(n)); (-1)^sum(i=1, matsize(F)[1], F[i, 2])} {Lucas(n)=fibonacci(n-1)+fibonacci(n+1)} {a(n)=polcoeff(sum(m=1, n, lambda(m)*fibonacci(m)*x^m/(1-Lucas(m)*x^m+(-1)^m*x^(2*m)+x*O(x^n))), n)} CROSSREFS Cf. A203847, A054783, A008836 (lambda), A000204 (Lucas), A000045. Cf. A209614 (variant). Sequence in context: A108707 A046775 A221787 * A085393 A128980 A096693 Adjacent sequences:  A204057 A204058 A204059 * A204061 A204062 A204063 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 12 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 14 08:20 EDT 2020. Contains 336480 sequences. (Running on oeis4.)