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 A382640 #16 Apr 13 2025 21:43:40
%S A382640 1,4,16,61,217,706,2074,5461,12961,28072,56236,105469,187081,316486,
%T A382640 514102,806341,1226689,1816876,2628136,3722557,5174521,7072234,
%U A382640 9519346,12636661,16563937,21461776,27513604,34927741,43939561,54813742,67846606,83368549,101746561
%N A382640 a(n) = 90*binomial(n,6) + 90*binomial(n,5) + 54*binomial(n,4) + 24*binomial(n,3) + 9*binomial(n,2) + 3*n + 1.
%C A382640 a(n) is the number of words of length n defined on 4 symbols where three chosen symbols (say, the three largest ones) are used at most twice.
%H A382640 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A382640 a(n) = 37 - 94*(n+1) + (187/2)*(n+1)^2 - (373/8)*(n+1)^3 + (103/8)*(n+1)^4 - (15/8)*(n+1)^5 + (1/8)*(n+1)^6.
%F A382640 E.g.f.: (1 + x + x^2/2)^3*exp(x).
%F A382640 G.f.: (1 - 3*x + 9*x^2 - 2*x^3 + 21*x^4 + 27*x^5 + 37*x^6)/(1 - x)^7. - _Stefano Spezia_, Apr 01 2025
%e A382640 a(3) = 61 since from the 64 words defined on {0, 1, 2, 3} we subtract the three words 111, 222, 333.
%Y A382640 Cf. A382618.
%K A382640 nonn,easy
%O A382640 0,2
%A A382640 _Enrique Navarrete_, Apr 01 2025