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%I #14 May 17 2021 15:29:04
%S 1,1,1,1,0,1,1,1,1,0,-1,1,1,1,2,-1,-3,1,1,2,5,-3,-7,1,0,5,13,-7,-15,0,
%T -5,13,33,-15,-30,-5,-23,33,81,-30,-55,-23,-79,81,192,-55,-87,-79,
%U -239,192,439,-87,-95,-239,-670,439,965,-95,49,-670,-1779,965,2025,49,768
%N a(n) = Sum_{i=n-4..n-1} (-1)^i*a(i), a(1)=1, a(2)=1, a(3)=1, a(4)=1.
%H Reinhard Zumkeller, <a href="/A051793/b051793.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,-1,0,-1,0,1,0,1).
%F a(0)=1, a(1)=1, a(2)=1, a(3)=1, a(4)=0, a(5)=1, a(6)=1, a(7)=1,
%F a(n) = -a(n-2)-a(n-4)+a(n-6)+a(n-8). - _Harvey P. Dale_, Sep 14 2012
%F G.f.: -x*(x^2+1)*(2*x^5+x^4+x^3+x^2+x+1) / (x^8+x^6-x^4-x^2-1). - _Colin Barker_, Mar 17 2015
%t RecurrenceTable[{a[1]==a[2]==a[3]==a[4]==1,a[n]==Sum[(-1)^i a[i],{i,n-4,n-1}]},a,{n,70}] (* or *) LinearRecurrence[{0, -1, 0, -1, 0, 1, 0, 1}, {1, 1, 1, 1, 0, 1, 1, 1}, 70] (* _Harvey P. Dale_, Sep 14 2012 *)
%o (Haskell)
%o a051793 n = a051793_list !! (n-1)
%o a051793_list = 1 : 1 : 1 : 1 : f [1, 1, 1, 1] [-1, 1, -1, 1] where
%o f xs'@(x:xs) as'@(a:as) = y : f (xs ++ [y]) (as ++ [a]) where
%o y = sum $ zipWith (*) xs' as'
%o -- _Reinhard Zumkeller_, Dec 16 2013
%o (PARI) Vec(-x*(x^2+1)*(2*x^5+x^4+x^3+x^2+x+1)/(x^8+x^6-x^4-x^2-1) + O(x^100)) \\ _Colin Barker_, Mar 17 2015
%K easy,nice,sign
%O 1,15
%A Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 10 1999
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