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 A203838 a(n) = sigma_3(n)*Fibonacci(n), where sigma_3(n) = A001158(n), the sum of cubes of divisors of n. 4
 1, 9, 56, 219, 630, 2016, 4472, 12285, 25738, 62370, 118548, 294336, 512134, 1167192, 2152080, 4620147, 7847658, 17604792, 28681660, 62224470, 105431872, 212319468, 348698376, 759507840, 1181718775, 2401396326, 4014783920, 7980869832, 12542045310 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Compare g.f. to the Lambert series identity: Sum_{n>=1} n^3*x^n/(1-x^n) = Sum_{n>=1} sigma_3(n)*x^n. LINKS FORMULA G.f.: Sum_{n>=1} n^3*fibonacci(n)*x^n/(1 - Lucas(n)*x^n + (-1)^n*x^(2*n)) = Sum_{n>=1} sigma_3(n)*fibonacci(n)*x^n, where Lucas(n) = A000204(n). EXAMPLE G.f.: A(x) = x + 9*x^2 + 56*x^3 + 219*x^4 + 630*x^5 + 2016*x^6 +... where A(x) = x/(1-x-x^2) + 2^3*1*x^2/(1-3*x^2+x^4) + 3^3*2*x^3/(1-4*x^3-x^6) + 4^3*3*x^4/(1-7*x^4+x^8) + 5^3*5*x^5/(1-11*x^5-x^10) + 6^3*8*x^6/(1-18*x^6+x^12) +...+ n^3*fibonacci(n)*x^n/(1 - Lucas(n)*x^n + (-1)^n*x^(2*n)) +... PROG (PARI) {a(n)=sigma(n, 3)*fibonacci(n)} (PARI) {Lucas(n)=fibonacci(n-1)+fibonacci(n+1)} {a(n)=polcoeff(sum(m=1, n, m^3*fibonacci(m)*x^m/(1-Lucas(m)*x^m+(-1)^m*x^(2*m)+x*O(x^n))), n)} CROSSREFS Cf. A203847, A203848, A203849, A001158 (sigma_3), A000204 (Lucas), A000045. Sequence in context: A245488 A242604 A212150 * A097556 A196861 A211844 Adjacent sequences:  A203835 A203836 A203837 * A203839 A203840 A203841 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 12 2012 STATUS approved

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Last modified August 11 17:27 EDT 2020. Contains 336428 sequences. (Running on oeis4.)