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 A382618 #15 Apr 13 2025 18:55:51
%S A382618 1,4,16,63,243,918,3402,12393,44469,157464,551124,1909251,6554439,
%T A382618 22320522,75464622,253497357,846585513,2812385772,9298091736,
%U A382618 30606218631,100341906651,327757733694,1066956026706,3462376910193,11203038280413,36150980669568,116360969030172
%N A382618 a(n) = 3^(n-2)*(binomial(n,2) + 3*n + 9).
%C A382618 a(n) is the number of words of length n defined on 4 letters where a chosen letter (for example, the first letter of the alphabet) is used at most twice.
%H A382618 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-27,27).
%F A382618 E.g.f.: (1 + x + x^2/2)*exp(3*x).
%F A382618 G.f.: x*(1 - 5*x + 7*x^2)/(1 - 3*x)^3. - _Stefano Spezia_, Apr 01 2025
%e A382618 a(4) = 243 since from the 256 words defined on {0, 1, 2, 3} we subtract the 4 words of type 0001, the 4 words of type 0002, the 4 words of type 0003, and 0000.
%t A382618 a[n_] := 3^(n-2)*(n^2 + 5*n + 18)/2; Array[a, 27, 0] (* _Amiram Eldar_, Apr 01 2025 *)
%Y A382618 Cf. A006234.
%K A382618 nonn,easy
%O A382618 0,2
%A A382618 _Enrique Navarrete_, Apr 01 2025