A255985 a(n) = 1 for n <= 6; a(n) = 49*a(n-1) - 882*a(n-2) + 8820*a(n-3) - 52920*a(n-4) + 190512*a(n-5) - 381024*a(n-6) + 326592*a(n-7) otherwise.

1, 1, 1, 1, 1, 1, 1, 91147, 4557301, 143008075, 3791855893, 95039848267, 2350059062869, 58037421216523, 1434206075225749, 35454497256469963, 876533685507121621, 21670381641194181259, 535748905642908896533, 13245082208240954261323

Offset: 0

Author

Alexander Samokrutov, Mar 13 2015

Keywords

• nonn
• easy

Comments

a(n)/a(n-1) tends to 24.7225... = 7 + 7^(1/7) + 7^(2/7) + 7^(3/7) + 7^(4/7) + 7^(5/7) + 7^(6/7).

In general, the polynomial x^7 - k7*x^6 - k6*x^5 - k5*x^4 - k4*x^3 - k3*x^2 - k2*x - k1 has a root r + b*m^(1/7) + c*m^(2/7) + d*m^(3/7) + e*m^(4/7) + g*m^(5/7) + h*m^(6/7), see links for coefficients k1, k2, k3, k4, k5, k6, k7.

Links

• Colin Barker, Table of n, a(n) for n = 0..720
• Alexander Samokrutov, Coefficients k1, k2, k3, k4, k5, k6, k7
• Index entries for linear recurrences with constant coefficients, signature (49,-882,8820,-52920,190512,-381024,326592).

Crossrefs

Cf. A247344, A255983.

Programs

Magma

[n le 7 select 1 else 49*Self(n-1)-882*Self(n-2)+8820*Self(n-3)-52920*Self(n-4)+190512*Self(n-5) -381024*Self(n-6) +326592*Self(n-7): n in [1..30]]; // Vincenzo Librandi, Mar 21 2015

Mathematica

LinearRecurrence[{49, -882, 8820, -52920, 190512, -381024, 326592}, {1, 1, 1, 1, 1, 1, 1}, 20] (* Vincenzo Librandi, Mar 21 2015 *)

PARI

Vec(-(235446*x^6 -145578*x^5 +44934*x^4 -7986*x^3 +834*x^2 -48*x +1) / (326592*x^7 -381024*x^6 +190512*x^5 -52920*x^4 +8820*x^3 -882*x^2 +49*x -1) + O(x^100)) \\ Colin Barker, Mar 13 2015

Formula

a(n) = 49*a(n-1) -882*a(n-2) +8820*a(n-3) -52920*a(n-4) +190512*a(n-5) -381024*a(n-6) +326592*a(n-7).

G.f.: -(235446*x^6 -145578*x^5 +44934*x^4 -7986*x^3 +834*x^2 -48*x +1) / (326592*x^7 -381024*x^6 +190512*x^5 -52920*x^4 +8820*x^3 -882*x^2 +49*x -1). - Colin Barker, Mar 13 2015