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%I #44 Sep 08 2022 08:46:11
%S 1,1,1,1,1,1,1,91147,4557301,143008075,3791855893,95039848267,
%T 2350059062869,58037421216523,1434206075225749,35454497256469963,
%U 876533685507121621,21670381641194181259,535748905642908896533,13245082208240954261323
%N 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.
%C 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).
%C 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.
%H Colin Barker, <a href="/A255985/b255985.txt">Table of n, a(n) for n = 0..720</a>
%H Alexander Samokrutov, <a href="/A255985/a255985_1.txt">Coefficients k1, k2, k3, k4, k5, k6, k7</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (49,-882,8820,-52920,190512,-381024,326592).
%F 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).
%F 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
%t LinearRecurrence[{49, -882, 8820, -52920, 190512, -381024, 326592}, {1, 1, 1, 1, 1, 1, 1}, 20] (* _Vincenzo Librandi_, Mar 21 2015 *)
%o (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
%o (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
%Y Cf. A247344, A255983.
%K nonn,easy
%O 0,8
%A _Alexander Samokrutov_, Mar 13 2015
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