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 A344215 #12 Mar 13 2022 12:47:43
%S A344215 0,0,2,15,76,325,1266,4655,16472,56745,191710,638275,2101188,6855485,
%T A344215 22205834,71498775,229058224,730680145,2322163638,7356008555,
%U A344215 23234743580,73200452325,230081633122,721667902015,2259234965256,7060318981625,22028631430286,68628565425555,213512971483252
%N A344215 a(n) = n*(3^(n-1) - 2^(n-1)).
%C A344215 a(n) is the number of quaternary strings of length n that contain one 0 and at least one 1.
%C A344215 For ternary strings with this property see A058877; for binary strings see A199969.
%H A344215 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (10,-37,60,-36).
%F A344215 E.g.f.: x*(exp(3*x) - exp(2*x)).
%F A344215 G.f.: x^2*(2 - 5*x)/(1 - 5*x + 6*x^2)^2. - _Stefano Spezia_, May 12 2021
%e A344215 a(3)=15 since the strings are the 3 permutations of 011, the 6 permutations of 012 and the 6 permutations of 013.
%t A344215 LinearRecurrence[{10, -37, 60, -36}, {0, 0, 2, 15}, 29] (* _Amiram Eldar_, May 11 2021 *)
%t A344215 Table[n(3^(n-1)-2^(n-1)),{n,0,30}] (* _Harvey P. Dale_, Mar 13 2022 *)
%Y A344215 Cf. A058877, A199969.
%K A344215 nonn,easy
%O A344215 0,3
%A A344215 _Enrique Navarrete_, May 11 2021