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%I #10 Jan 04 2024 04:13:31
%S 1,1,2,7,17,44,117,305,798,2091,5473,14328,37513,98209,257114,673135,
%T 1762289,4613732,12078909,31622993,82790070,216747219,567451585,
%U 1485607536,3889371025,10182505537,26658145586,69791931223,182717648081
%N Anti-diagonal sums of number triangle A086645.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,2,-1).
%F G.f.: (1-x-x^2)/(1-2x-x^2-2x^3+x^4); a(n)=2(n-1)+a(n-2)+2a(n-3)-a(n-4); a(n)=sum{k=0..floor(n/2), C(2(n-k), 2k)}; a(n)=sum{k=0..floor(n/2), sum{j=0..n-k, C(2(n-2k), j)C(2k, j)}}.
%t LinearRecurrence[{2,1,2,-1},{1,1,2,7},30] (* _Harvey P. Dale_, Jun 01 2021 *)
%K easy,nonn
%O 0,3
%A _Paul Barry_, Jun 04 2005
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