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A214829 a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 7.

%I A214829 #27 Sep 08 2022 08:46:02
%S A214829 1,7,7,15,29,51,95,175,321,591,1087,1999,3677,6763,12439,22879,42081,
%T A214829 77399,142359,261839,481597,885795,1629231,2996623,5511649,10137503,
%U A214829 18645775,34294927,63078205,116018907,213392039,392489151,721900097,1327781287,2442170535
%N A214829 a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 7.
%C A214829 See comments in A214727.
%H A214829 Robert Price, <a href="/A214829/b214829.txt">Table of n, a(n) for n = 0..1000</a>
%H A214829 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1).
%F A214829 G.f.: (1+6*x-x^2)/(1-x-x^2-x^3).
%F A214829 a(n) = -A000073(n) + 6*A000073(n+1) + A000073(n+2). - _G. C. Greubel_, Apr 24 2019
%t A214829 LinearRecurrence[{1,1,1}, {1,7,7}, 40] (* _G. C. Greubel_, Apr 24 2019 *)
%o A214829 (PARI) Vec((x^2-6*x-1)/(x^3+x^2+x-1) + O(x^40)) \\ _Michel Marcus_, Jun 04 2017
%o A214829 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+6*x-x^2)/(1-x-x^2-x^3) )); // _G. C. Greubel_, Apr 24 2019
%o A214829 (Sage) ((1+6*x-x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 24 2019
%o A214829 (GAP) a:=[1,7,7];; 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 A214829 Cf. A000213, A000288, A000322, A000383, A060455, A136175, A141036, A141523, A214825, A214826, A214827, A214828, A214830, A214831.
%K A214829 nonn,easy
%O A214829 0,2
%A A214829 _Abel Amene_, Aug 07 2012