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 A383623 #10 May 08 2025 22:26:28
%S A383623 0,0,2,20,128,672,3168,14016,59648,247808,1014272,4113408,16588800,
%T A383623 66674688,267444224,1071497216,4289921024,17168596992,68694441984,
%U A383623 274822594560,1099389992960,4397780172800,17591605133312,70367481692160,281472242024448
%N A383623 a(n) = 4^n - (n^2 + 3*n + 4)*2^(n-2).
%C A383623 a(n) is the number of strings of length n defined on {0,1,2,3} that contain at least two 2s or at least two 3s (or both).
%H A383623 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (10,-36,56,-32).
%F A383623 E.g.f.: exp(4*x) - exp(2*x)*(1+x)^2.
%F A383623 a(n) = 4^n - A007466(n+1).
%F A383623 G.f.: 2*x^2/((1 - 2*x)^3*(1 - 4*x)). - _Stefano Spezia_, May 03 2025
%e A383623 a(3)=20 since the strings are 220 (3 of this type), 221 (3 of this type), 223 (3 of this type), 330 (3 of this type), 331 (3 of this type), 332 (3 of this type), 222 and 333.
%Y A383623 Cf. A000302, A007466.
%K A383623 nonn,easy
%O A383623 0,3
%A A383623 _Enrique Navarrete_, May 03 2025