A214830 - OEIS

%I #27 Sep 08 2022 08:46:02

%S 1,8,8,17,33,58,108,199,365,672,1236,2273,4181,7690,14144,26015,47849,

%T 88008,161872,297729,547609,1007210,1852548,3407367,6267125,11527040,

%U 21201532,38995697,71724269,131921498,242641464,446287231,820850193,1509778888

%N a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 8.

%C See comments in A214727.

%H Robert Price, <a href="/A214830/b214830.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1).

%F G.f.: (1+7*x-x^2)/(1-x-x^2-x^3).

%F a(n) = -A000073(n) + 7*A000073(n+1) + A000073(n+2). - _G. C. Greubel_, Apr 24 2019

%t CoefficientList[Series[(x^2-7*x-1)/(x^3+x^2+x-1), {x, 0, 40}], x] (* _Wesley Ivan Hurt_, Jun 18 2014 *)

%t LinearRecurrence[{1,1,1}, {1,8,8}, 40] (* _G. C. Greubel_, Apr 24 2019 *)

%o (PARI) my(x='x+O('x^40)); Vec((1+7*x-x^2)/(1-x-x^2-x^3)) \\ _G. C. Greubel_, Apr 24 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+7*x-x^2)/(1-x-x^2-x^3) )); // _G. C. Greubel_, Apr 24 2019

%o (Sage) ((1+7*x-x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 24 2019

%o (GAP) a:=[1,8,8];; for n in [4..40] do a[n]:=a[n-1]+a[n-2]+a[n-3]; od; a; # _G. C. Greubel_, Apr 24 2019

%Y Cf. A000213, A000288, A000322, A000383, A060455, A136175, A141036, A141523, A214825-A214831.

%K nonn,easy

%O 0,2

%A _Abel Amene_, Aug 07 2012