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%I #19 Jul 04 2019 10:30:28
%S 1,2,4,8,16,31,61,117,228,436,845,1615,3120,5965,11501,22001,42365,
%T 81091,156010,298777,574450,1100620,2115150,4053959,7788126,14931102,
%U 28676899,54990202,105594073,202519004,388825095,745825185,1431776536,2746639052
%N Sums of antidiagonals of A223968.
%H Harvey P. Dale, <a href="/A223940/b223940.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-3,-3,1).
%F G.f.: (1-x) * (1+2*x-x^3) / (1-x-4*x^2+3*x^3+3*x^4-x^5).
%F a(n) = a(n-1) + 4*a(n-2) - 3*a(n-3) - 3*a(n-4) + a(n-5) with a(0) = 1, a(1) = 2, a(2) = 4, a(3) = 8, a(4) = 16, a(5) = 31.
%F a(n) = Sum_{k=0..n} A223968(n-k, k).
%t CoefficientList[Series[(1-x)(1+2x-x^3)/(1-x-4x^2+3x^3+3x^4-x^5), {x,0,40}],x] (* or *) LinearRecurrence[{1,4,-3,-3,1},{1,2,4,8,16},40] (* _Harvey P. Dale_, Jul 04 2019 *)
%Y Cf. A223968
%K nonn,easy
%O 0,2
%A _Philippe Deléham_, Mar 29 2013
%E a(32) corrected by _Sean A. Irvine_, May 19 2019
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