This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%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