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 A384536 #10 Jun 09 2025 10:40:06
%S A384536 1,4,16,64,256,1024,4081,16174,63856,252064,998176,3972544,15890176,
%T A384536 63814144,256903936,1035303424,4171964416,16799678464,67578904576,
%U A384536 271543926784,1089985970176,4371374669824,17518838480896,70170274299904,280945723703296
%N A384536 a(n) = 4^n - 2^(n-6)*15*binomial(n,6).
%C A384536 a(n) is the number of strings of length n defined on {0, 1, 2, 3} that do not contain exactly two 2's and exactly four 3's.
%H A384536 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (18,-140,616,-1680,2912,-3136,1920,-512).
%F A384536 G.f.: (1 - 14*x + 84*x^2 - 280*x^3 + 560*x^4 - 672*x^5 + 433*x^6 - 68*x^7)/((1 - 2*x)^7*(1 - 4*x)). - _Stefano Spezia_, Jun 02 2025
%e A384536 a(8) = 63856 since from the 65536 strings of length 8 we subtract the 420 permutations of 33332200, the 840 permutations of 33332201 and the 420 permutations of 33332211.
%t A384536 a[n_]:=4^n-2^(n-6)*15*Binomial[n,6];Array[a,25,0] (* or *)
%t A384536 LinearRecurrence[{18,-140,616,-1680,2912,-3136,1920,-512},{1, 4, 16, 64, 256, 1024, 4081, 16174},25] (* or *)
%t A384536 CoefficientList[Series[ (1 - 14*x + 84*x^2 - 280*x^3 + 560*x^4 - 672*x^5 + 433*x^6 - 68*x^7)/((1 - 2*x)^7*(1 - 4*x)),{x,0,24}],x] (* _James C. McMahon_, Jun 08 2025 *)
%Y A384536 Cf. A384506.
%K A384536 nonn,easy
%O A384536 0,2
%A A384536 _Enrique Navarrete_, Jun 02 2025