%I #8 Jul 31 2015 18:12:30
%S 1,3,10,35,127,472,1781,6783,25978,99823,384331,1481424,5714073,
%T 22048715,85098282,328485899,1268080423,4895497064,18899853101,
%U 72967061671,281708048154,1087611942455,4199040207827,16211637659168
%N Expansion of (1-3x)/(1-6x+8x^2+x^3).
%C Diagonal sums of A114195.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6, -8, -1).
%F a(n)=6a(n-1)-8a(n-2)-a(n-3); a(n)=sum{k=0..floor(n/2), sum{j=0..n-k, C(n-k, j)C(j+k, 2k)2^(j-k)}}.
%t CoefficientList[Series[(1-3x)/(1-6x+8x^2+x^3),{x,0,30}],x] (* or *) LinearRecurrence[{6,-8,-1},{1,3,10},30] (* _Harvey P. Dale_, Feb 02 2012 *)
%K easy,nonn
%O 0,2
%A _Paul Barry_, Nov 16 2005