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%I A115714 #19 Dec 14 2023 05:33:00
%S A115714 1,-1,-3,0,1,-5,1,0,-3,-1,1,-4,1,-1,-3,0,1,-5,1,0,-3,-1,1,-4,1,-1,-3,
%T A115714 0,1,-5,1,0,-3,-1,1,-4,1,-1,-3,0,1,-5,1,0,-3,-1,1,-4,1,-1,-3,0,1,-5,1,
%U A115714 0,-3,-1,1,-4,1,-1,-3,0,1,-5,1,0,-3,-1,1,-4
%N A115714 Periodic {1,-1,-3,0,1,-5,1,0,-3,-1,1,-4}.
%C A115714 Diagonal sums of number triangle A115713.
%H A115714 G. C. Greubel, <a href="/A115714/b115714.txt">Table of n, a(n) for n = 0..1000</a>
%H A115714 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1,0,1,1,1)
%F A115714 G.f.: (1 - 3*x^2 + 4*x^3 + 3*x^4 + 4*x^5)/(1 + x + x^2 - x^4 - x^5 - x^6).
%F A115714 a(n) = Sum_{k=0..floor(n/2)} A115713(n-k, k).
%t A115714 LinearRecurrence[{-1,-1,0,1,1,1}, {1,-1,-3,0,1,-5}, 80] (* _G. C. Greubel_, Nov 23 2021 *)
%o A115714 (Sage)
%o A115714 def A115714_list(prec):
%o A115714     P.<x> = PowerSeriesRing(ZZ, prec)
%o A115714     return P( (1-3*x^2+4*x^3+3*x^4+4*x^5)/(1+x+x^2-x^4-x^5-x^6) ).list()
%o A115714 A115714_list(80) # _G. C. Greubel_, Nov 23 2021
%Y A115714 Cf. A115713.
%K A115714 easy,sign
%O A115714 0,3
%A A115714 _Paul Barry_, Jan 29 2006

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