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A277252 a(n) = a(n-2) + a(n-3) + a(n-4) with a(0) = 0, a(1) = a(2) = 1, a(3) = 0.

%I A277252 #26 May 03 2017 08:43:26
%S A277252 0,1,1,0,2,2,3,4,7,9,14,20,30,43,64,93,137,200,294,430,631,924,1355,
%T A277252 1985,2910,4264,6250,9159,13424,19673,28833,42256,61930,90762,133019,
%U A277252 194948,285711,418729,613678,899388,1318118,1931795,2831184,4149301,6081097,8912280,13061582,19142678,28054959
%N A277252 a(n) = a(n-2) + a(n-3) + a(n-4) with a(0) = 0, a(1) = a(2) = 1, a(3) = 0.
%C A277252 Limit a(n+1)/a(n) = 1.465571...  (as in Narayana's cows sequence A000930).
%H A277252 G. C. Greubel, <a href="/A277252/b277252.txt">Table of n, a(n) for n = 0..1000</a>
%H A277252 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,1).
%F A277252 a(n) = a(n - 2) + a(n - 3) + a(n - 4).
%F A277252 G.f.: x*(1 + x - x^2)/(1 - x^2 - x^3 - x^4).
%F A277252 a(n) + A277253(n) = A000930(n).
%p A277252 a:= n-> (<<0|1|0|0>, <0|0|1|0>,
%p A277252           <0|0|0|1>, <1|1|1|0>>^n. <<0,1,1,0>>)[1,1]:
%p A277252 seq(a(n), n=0..50);  # _Alois P. Heinz_, Oct 07 2016
%t A277252 CoefficientList[Series[x*(1 + x - x^2)/(1 - x^2 - x^3 - x^4), {x, 0, 50}], x]
%t A277252 RecurrenceTable[{a[n] == a[n - 2] + a[n - 3] + a[n - 4], a[1] == 0,  a[2] == a[3] == 1, a[4] == 0}, a, {n, 52}]
%t A277252 LinearRecurrence[{0, 1, 1,1}, {0,1, 1, 0},52]
%o A277252 (PARI) x='x+O('x^50); concat([0], Vec(x*(1+x-x^2)/(1-x^2-x^3-x^4))) \\ _G. C. Greubel_, May 02 2017
%Y A277252 Summed to A277253 equals A000930.
%K A277252 nonn
%O A277252 0,5
%A A277252 _Nicolas Bègue_, Oct 07 2016
%E A277252 Corrected G.f. - _G. C. Greubel_, May 02 2017