%I #10 Oct 18 2021 18:03:13
%S 1,2,6,13,30,62,133,270,558,1125,2286,4590,9253,18542,37230,74533,
%T 149358,298862,598309,1196910,2394990,4790565,9583470,19168110,
%U 38340901,76684142,153377646,306759973,613538670,1227086702,2454210853
%N Diagonal sums of "correlation triangle" for 2^n.
%C Diagonal sums of number triangle A003983.
%H Harvey P. Dale, <a href="/A115217/b115217.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 (2,2,-3,-2,-2,4).
%F a(n)=sum{k=0..floor(n/2), sum{j=0..n-k, [j<=k]*2^(k-j)[j<=n-2k]2^(n-2k-j)}}.
%F G.f.: 1/((1-2x)(1-2x^2)(1-x^3)); a(n)=2a(n-1)+2a(n-2)-3a(n-3)-2a(n-4)-2a(n-5)+4a(n-6); - _Paul Barry_, Jan 18 2006
%t LinearRecurrence[{2,2,-3,-2,-2,4},{1,2,6,13,30,62},40] (* _Harvey P. Dale_, Oct 18 2021 *)
%K easy,nonn
%O 0,2
%A _Paul Barry_, Jan 16 2006