A203848 a(n) = sigma(n)*Fibonacci(n), where sigma(n) = A000203(n), the sum of divisors of n.
1, 3, 8, 21, 30, 96, 104, 315, 442, 990, 1068, 4032, 3262, 9048, 14640, 30597, 28746, 100776, 83620, 284130, 350272, 637596, 687768, 2782080, 2325775, 5098506, 7856720, 17797416, 15426870, 59906880, 43080608, 137233467, 169179744, 307955898, 442918320, 1358662032
Offset: 1
Examples
G.f.: A(x) = x + 3*x^2 + 8*x^3 + 21*x^4 + 30*x^5 + 96*x^6 + 104*x^7 +... where A(x) = x/(1-x-x^2) + 2*1*x^2/(1-3*x^2+x^4) + 3*2*x^3/(1-4*x^3-x^6) + 4*3*x^4/(1-7*x^4+x^8) + 5*5*x^5/(1-11*x^5-x^10) + 6*8*x^6/(1-18*x^6+x^12) +...+ n*fibonacci(n)*x^n/(1 - Lucas(n)*x^n + (-1)^n*x^(2*n)) +...
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Programs
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Magma
[DivisorSigma(1, n)*Fibonacci(n): n in [1..40]]; // Vincenzo Librandi, Aug 12 2016
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Mathematica
Table[DivisorSigma[1, n] Fibonacci[n], {n, 40}] (* Wesley Ivan Hurt, Aug 10 2016 *) -
PARI
{a(n)=sigma(n)*fibonacci(n)} -
PARI
{Lucas(n)=fibonacci(n-1)+fibonacci(n+1)} {a(n)=polcoeff(sum(m=1,n,m*fibonacci(m)*x^m/(1-Lucas(m)*x^m+(-1)^m*x^(2*m)+x*O(x^n))),n)}
Formula
G.f.: Sum_{n>=1} n*fibonacci(n)*x^n/(1 - Lucas(n)*x^n + (-1)^n*x^(2*n)) = Sum_{n>=1} sigma(n)*fibonacci(n)*x^n, where Lucas(n) = A000204(n).
Comments