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 A129362 a(n) = sum{k=floor((n+1)/2)..n, J(k+1)}, J(n) = A001045(n). 3

%I

%S 1,1,4,8,19,37,80,160,331,661,1344,2688,5419,10837,21760,43520,87211,

%T 174421,349184,698368,1397419,2794837,5591040,11182080,22366891,

%U 44733781,89473024,178946048,357903019,715806037

%N a(n) = sum{k=floor((n+1)/2)..n, J(k+1)}, J(n) = A001045(n).

%H Harvey P. Dale, <a href="/A129362/b129362.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-1,0,-2,-4)

%F G.f.: (1+2x^3)/((1-x-2x^2)(1-x^2-2x^4)).

%F a(n) = a(n-1) + 3a(n-2) - a(n-3) - 2a(n-5) - 4a(n-6).

%F a(n) = sum{k=0..floor(n/2), J(n-k+1)}.

%F a(n) = sum{k=0..n, J(k+1)-J((k+1)/2)(1-(-1)^k)/2}.

%F a(n) = sum{k=0..n, J(k+1)}-sum{k=0..floor((n-1)/2), J(k+1)}.

%t LinearRecurrence[{1,3,-1,0,-2,-4},{1,1,4,8,19,37},30] (* _Harvey P. Dale_, Oct 22 2011 *)

%Y Cf. A129361.

%K easy,nonn

%O 0,3

%A _Paul Barry_, Apr 11 2007

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Last modified December 3 16:20 EST 2020. Contains 338906 sequences. (Running on oeis4.)