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 A099530 #14 Apr 13 2023 16:27:45 %S A099530 1,1,1,1,0,-1,-2,-3,-3,-2,0,3,6,8,8,5,-1,-9,-17,-22,-21,-12,5,27,48, %T A099530 60,55,28,-20,-80,-135,-163,-143,-63,72,235,378,441,369,134,-244,-685, %U A099530 -1054,-1188,-944,-259,795,1983,2927,3186,2391,408,-2519,-5705,-8096,-8504,-5985,-280,7816,16320,22305,22585,14769 %N A099530 Expansion of 1/(1 - x + x^4). %C A099530 Binomial transform of A099531. %H A099530 G. C. Greubel, <a href="/A099530/b099530.txt">Table of n, a(n) for n = 0..1000</a> %H A099530 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,-1). %F A099530 a(n) = a(n-1) - a(n-4). %F A099530 a(n) = Sum_{k=0..floor(n/4)} binomial(n-3*k, k)*(-1)^k. %t A099530 LinearRecurrence[{1,0,0,-1}, {1,1,1,1}, 80] (* _G. C. Greubel_, Apr 13 2023 *) %o A099530 (Magma) [n le 4 select 1 else Self(n-1) -Self(n-4): n in [1..81]]; // _G. C. Greubel_, Apr 13 2023 %o A099530 (SageMath) %o A099530 @CachedFunction %o A099530 def a(n): # a = A099530 %o A099530 if (n<4): return 1 %o A099530 else: return a(n-1) - a(n-4) %o A099530 [a(n) for n in range(81)] # _G. C. Greubel_, Apr 13 2023 %Y A099530 Cf. A050935, A099531. %K A099530 easy,sign %O A099530 0,7 %A A099530 _Paul Barry_, Oct 20 2004