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A277253 a(n) = a(n-2) + a(n-3) + a(n-4) for n>3, a(0)=1, a(1)=a(2)=0, a(3)=2.

%I A277253 #26 Jun 10 2023 11:49:41
%S A277253 1,0,0,2,1,2,3,5,6,10,14,21,30,45,65,96,140,206,301,442,647,949,1390,
%T A277253 2038,2986,4377,6414,9401,13777,20192,29592,43370,63561,93154,136523,
%U A277253 200085,293238,429762,629846,923085,1352846,1982693,2905777,4258624,6241316,9147094,13405717,19647034,28794127,42199845
%N A277253 a(n) = a(n-2) + a(n-3) + a(n-4) for n>3, a(0)=1, a(1)=a(2)=0, a(3)=2.
%C A277253 a(n+1)/a(n) = 1.465571... like Narayana's cows sequence A000930.
%H A277253 G. C. Greubel, <a href="/A277253/b277253.txt">Table of n, a(n) for n = 0..1000</a>
%H A277253 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,1).
%F A277253 G.f.: (1 - x^2 + x^3)/((1 + x)*(1 - x - x^3)).
%p A277253 a:= n-> (<<0|1|0|0>, <0|0|1|0>,
%p A277253           <0|0|0|1>, <1|1|1|0>>^n. <<1,0,0,2>>)[1,1]:
%p A277253 seq(a(n), n=0..50);  # _Alois P. Heinz_, Oct 07 2016
%t A277253 RecurrenceTable[{a[n] == a[n - 2] + a[n - 3] + a[n - 4], a[1] ==1,  a[2] == a[3] == 0, a[4] == 2}, a, {n, 50}]
%t A277253 LinearRecurrence[{0, 1, 1, 1}, {1, 0, 0, 2}, 52]
%t A277253 CoefficientList[Series[(-1 + x^2 - x^3)/(-1 + x^2 + x^3 + x^4), {x, 0, 52}], x]
%t A277253 nxt[{a_,b_,c_,d_}]:={b,c,d,a+b+c}; NestList[nxt,{1,0,0,2},50][[;;,1]] (* _Harvey P. Dale_, Jun 10 2023 *)
%o A277253 (Magma) I:=[1,0,0,2]; [n le 4 select I[n] else Self(n-2)+Self(n-3)+Self(n-4): n in [1..50]]; // _Vincenzo Librandi_, Nov 07 2016
%Y A277253 Cf. A000930.
%K A277253 nonn,easy
%O A277253 0,4
%A A277253 _Nicolas Bègue_, Oct 07 2016