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A255983 a(n) = 1 for n <= 5; 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) otherwise. 5
1, 1, 1, 1, 1, 1, -4914, -181854, -4339944, -89153184, -1746815574, -33850986114, -655203251304, -12686085675144, -245683477042884, -4758284508073524, -92156792465163564, -1784855834560787004, -34568319709081645344, -669504074781304567584, -12966661247726595160224 (list; graph; refs; listen; history; text; internal format)
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

Cf. A247344, A255985.

Sequence in context: A114770 A013807 A013884 * A043480 A028550 A091878

Adjacent sequences:  A255980 A255981 A255982 * A255984 A255985 A255986

KEYWORD

sign,easy

AUTHOR

Alexander Samokrutov, Mar 13 2015

STATUS

approved

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Last modified September 17 22:53 EDT 2019. Contains 327147 sequences. (Running on oeis4.)