OFFSET
0,7
COMMENTS
a(n)/a(n-1) tends to 19.367561... = 6 + 6^(1/6) + 6^(2/6) + 6^(3/6) + 6^(4/6) + 6^(5/6), the largest real root of the polynomial x^6 - 36*x^5 + 450*x^4 - 3000*x^3 + 11250*x^2 - 22500*x + 18750.
In general, the polynomial x^6 - k6*x^5 - k5*x^4 - k4*x^3 - k3*x^2 - k2*x -k1 has a root r+b*m^(1/6)+c*m^(2/6)+d*m^(3/6)+g*m^(4/6)+h*m^(5/6), see links for coefficients k1, k2, k3, k4, k5, k6.
LINKS
Alexander Samokrutov, Table of n, a(n) for n = 0..25
Alexander Samokrutov, Coefficients k1, k2, k3, k4, k5, k6
Index entries for linear recurrences with constant coefficients, signature (36,-450,3000,-11250,22500,-18750).
FORMULA
a(n) = 36*a(n-1) - 450*a(n-2) + 3000*a(n-3) - 11250*a(n-4) + 22500*a(n-5) - 18750*a(n-6).
G.f.: -(13835*x^5-8665*x^4+2585*x^3-415*x^2+35*x-1) / (18750*x^6-22500*x^5+11250*x^4-3000*x^3+450*x^2-36*x+1). - Colin Barker, Mar 23 2015
MATHEMATICA
LinearRecurrence[{36, -450, 3000, -11250, 22500, -18750}, {1, 1, 1, 1, 1, 1}, 30] (* Vincenzo Librandi, Mar 21 2015 *)
PROG
(Magma) [n le 6 select 1 else 36*Self(n-1)-450*Self(n-2)+3000*Self(n-3)-11250*Self(n-4)+22500*Self(n-5)-18750*Self(n-6): n in [1..30]]; // Vincenzo Librandi, Mar 21 2015
(PARI) Vec(-(13835*x^5-8665*x^4+2585*x^3-415*x^2+35*x-1) / (18750*x^6-22500*x^5+11250*x^4-3000*x^3+450*x^2-36*x+1) + O(x^100)) \\ Colin Barker, Mar 23 2015
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Alexander Samokrutov, Mar 13 2015
STATUS
approved