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 A383953 #26 Aug 28 2025 10:24:05 %S A383953 4,7,15,29,59,117,235,469,939,1877,3755,7509,15019,30037,60075,120149, %T A383953 240299,480597,961195,1922389,3844779,7689557,15379115,30758229, %U A383953 61516459,123032917,246065835,492131669,984263339,1968526677,3937053355,7874106709,15748213419,31496426837 %N A383953 a(0) = 4, a(n) = 2*a(n-1) + (-1)^n. %H A383953 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,2). %F A383953 a(n) = (11*2^n + (-1)^n)/3. %F A383953 a(n) = A340627(n+1)/2. %F A383953 a(n) = 2*A052997(n) + 1 for n >= 1. %F A383953 a(n) = a(n-4) + 55*2^(n-4) for n >= 4. %F A383953 G.f.: (3*x + 4)/((x + 1)*(1 - 2*x)). %F A383953 E.g.f: (11*exp(2*x) + exp(-x))/3. %t A383953 a[n_] := (11*2^n + (-1)^n)/3; Array[a, 34, 0] (* _Amiram Eldar_, Aug 20 2025 *) %Y A383953 Cf. A005015, A052997, A340627. %Y A383953 Bisections give A199210 and A072261. %K A383953 nonn,easy,new %O A383953 0,1 %A A383953 _Paul Curtz_, Aug 19 2025