This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A130095 #11 Dec 11 2019 06:58:45
%S A130095 1,3,6,16,35,97,234,626,1603,4218,10947,28767,75026,196654,514269,
%T A130095 1346895,3524579,9229159,24157818,63250217,165580380,433505386,
%U A130095 1134903171,2971244450,7778742084,20365086102,53316292776,139584059112,365435296163,956722544582
%N A130095 Inverse Möbius transform of odd-indexed Fibonacci numbers.
%C A130095 Original name was: A051731 * A007436.
%C A130095 Conjecture: a(n)/a(n-1) tends to phi^2.
%F A130095 From _Peter Bala_, Mar 26 2015: (Start)
%F A130095 a(n) = sum {d | n} Fibonacci(2*d - 1).
%F A130095 O.g.f. Sum_{n >= 1} Fibonacci(2*n - 1)*x^n/(1 - x^n) = Sum_{n >= 1} x^n*(1 - x^n)/(1 - 3*x^n + x^(2*n)).
%F A130095 Sum_{n >= 1} a(n)*x^(2*n) = Sum_{n >= 1} x^n/( 1/(x^n - 1/x^n) - (x^n - 1/x^n) ).
%F A130095 For p prime, a(p) == k (mod p) where k = 3 if p == 2, 3 (mod 5), k = 2 if p == 1, 4 (mod 5) and k = 0 if p = 5. (End)
%e A130095 The divisors of 6 are 1, 2, 3 and 6. Hence
%e A130095 a(6) = Fibonacci(1) + Fibonacci(3) + Fibonacci(5) + Fibonacci(11) = 97.
%p A130095 #A130095
%p A130095 with(combinat): with(numtheory):
%p A130095 f := n -> fibonacci(2*n-1):
%p A130095 g := proc (n) local div; div := divisors(n):
%p A130095 add(f(div[j]), j = 1 .. tau(n)) end proc:
%p A130095 seq(g(n), n = 1 .. 30); # _Peter Bala_, Mar 26 2015
%Y A130095 Cf. A001519, A007435, A051731.
%K A130095 nonn,easy
%O A130095 1,2
%A A130095 _Gary W. Adamson_, May 06 2007
%E A130095 Incorrect original name removed and terms a(11) - a(30) added by _Peter Bala_, Mar 26 2015