A019484 - OEIS

%I #32 Sep 08 2022 08:44:44

%S 8,55,379,2612,18002,124071,855106,5893451,40618081,279942687,

%T 1929384798,13297456486,91647010581,631637678776,4353291555505,

%U 30003193292641,206784130187015,1425170850320396,9822378297435246,67696525926163327,466569244606302614

%N Expansion of (8 + 7 x - 7 x^2 - 7 x^3)/(1 - 6 x - 7 x^2 + 5 x^3 + 6 x^4).

%C Agrees with A010918 for terms 0 through 11055 but then differs from it.

%C a(11056) = 4971494197...7586894094 (9270 digits) = A010918(11056) - 1. - _Jianing Song_, Oct 15 2021

%D R. K. Guy, personal communication.

%H Vincenzo Librandi, <a href="/A019484/b019484.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,7,-5,-6).

%H <a href="/index/Se#sequences_which_agree_for_a_long_time">Index entries for sequences which agree for a long time but are different</a>

%F G.f.: (8 + 7 x - 7 x^2 - 7 x^3)/(1 - 6 x - 7 x^2 + 5 x^3 + 6 x^4).

%p - (8 + 7*x - 7*x^2 - 7*x^3) /(7*x^2 - 1 + 6*x - 6*x^4 - 5*x^3);

%t CoefficientList[ Series[(8 + 7 x - 7 x^2 - 7 x^3)/(1 - 6 x - 7 x^2 + 5 x^3 + 6 x^4), {x, 0, 18}], x] (* _Robert G. Wilson v_, May 16 2008 *)

%t LinearRecurrence[{6,7,-5,-6},{8,55,379,2612},20] (* _Harvey P. Dale_, Apr 20 2017 *)

%o (Magma) I:=[8,55,379,2612]; [n le 4 select I[n] else 6*Self(n-1)+7*Self(n-2)-5*Self(n-3)-6*Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Apr 21 2017

%Y Cf. A010918.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_.

%E The old definition was a(n) = 3*a(n-1) + a(n-2) - 2*a(n-3), but as _R. J. Mathar_ pointed out, this did not match the entries. I have therefore replaced the definition with a g.f. found by Superseeker. - _N. J. A. Sloane_, May 16 2008