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A098578 a(n) = Sum_{k=0..floor(n/4)} C(n-3*k,k+1).

%I A098578 #20 Feb 18 2024 05:18:19
%S A098578 0,1,2,3,4,6,9,13,18,25,35,49,68,94,130,180,249,344,475,656,906,1251,
%T A098578 1727,2384,3291,4543,6271,8656,11948,16492,22764,31421,43370,59863,
%U A098578 82628,114050,157421,217285,299914,413965,571387,788673,1088588,1502554
%N A098578 a(n) = Sum_{k=0..floor(n/4)} C(n-3*k,k+1).
%C A098578 Partial sums of A003269 (with leading zero).
%H A098578 G. C. Greubel, <a href="/A098578/b098578.txt">Table of n, a(n) for n = 0..1000</a>
%H A098578 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,1,-1)
%F A098578 G.f.: x/((1-x)^2-x^4(1-x)) = x / ((x-1)*(x^4+x-1)).
%F A098578 a(n) = 2*a(n-1) - a(n-2) + a(n-4) - a(n-5).
%F A098578 a(n) = a(n-1) + a(n-4) + 1.
%t A098578 CoefficientList[Series[x/((1-x)^2-x^4*(1-x)), {x,0,50}], x] (* or *) LinearRecurrence[{2,-1,0,1,-1}, {0,1,2,3,4}, 50] (* _G. C. Greubel_, Feb 03 2018 *)
%o A098578 (PARI) x='x+O('x^30); concat([0], Vec(x/((1-x)^2-x^4*(1-x)))) \\ _G. C. Greubel_, Feb 03 2018
%o A098578 (Magma) I:=[0,1,2,3,4]; [n le 5 select I[n] else 2*Self(n-1) - Self(n-2) + Self(n-4) - Self(n-5): n in [1..30]]; // _G. C. Greubel_, Feb 03 2018
%Y A098578 Cf. A077868.
%K A098578 easy,nonn
%O A098578 0,3
%A A098578 _Paul Barry_, Sep 16 2004