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A368346 a(n) = Sum_{k=0..n} 2^(n-k) * floor(k/4).

%I A368346 #23 Dec 22 2023 12:11:35
%S A368346 0,0,0,0,1,3,7,15,32,66,134,270,543,1089,2181,4365,8734,17472,34948,
%T A368346 69900,139805,279615,559235,1118475,2236956,4473918,8947842,17895690,
%U A368346 35791387,71582781,143165569,286331145,572662298,1145324604,2290649216,4581298440
%N A368346 a(n) = Sum_{k=0..n} 2^(n-k) * floor(k/4).
%H A368346 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,0,1,-3,2).
%F A368346 a(n) = a(n-4) + 2^(n-3) - 1.
%F A368346 a(n) = Sum_{k=0..n} floor(2^k/15).
%F A368346 a(n) = 3*a(n-1) - 2*a(n-2) + a(n-4) - 3*a(n-5) + 2*a(n-6).
%F A368346 G.f.: x^4/((1-x) * (1-2*x) * (1-x^4)).
%F A368346 a(n) = floor(2^(n+1)/15) - floor((n+1)/4).
%o A368346 (PARI) a(n, m=4, k=2) = (k^(n+1)\(k^m-1)-(n+1)\m)/(k-1);
%o A368346 (Python)
%o A368346 def A368346(n): return (1<<n+1)//15-(n+1>>2) # _Chai Wah Wu_, Dec 22 2023
%Y A368346 Partial sums of A083593.
%Y A368346 Cf. A178420, A178452, A178455, A178457, A178459, A178460, A178742.
%K A368346 nonn,easy
%O A368346 0,6
%A A368346 _Seiichi Manyama_, Dec 22 2023