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 A086443 #17 May 18 2022 02:30:49 %S A086443 0,0,1,10,67,376,1909,9094,41479,183412,792697,3367618,14120011, %T A086443 58605808,241331965,987648382,4022338063,16318934764,66007533313, %U A086443 266354656186,1072779614035,4314363685480,17330677214341,69552836627830 %N A086443 Expansion of x^2/((1-4*x)*(1-3*x)^2). %C A086443 Second binomial transform of A000295. Binomial transform of A066810 (with two leading zeros). %C A086443 a(n) is the number of n-digit sequences on 4 symbols that have at least two 0's. For ternary sequences see A066810 and for binary sequences see A000295. - _Enrique Navarrete_, Apr 15 2022 %H A086443 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (10,-33,36). %F A086443 a(n) = 4^n - 3^n - n*3^(n-1). %F A086443 E.g.f.: exp(3*x)*(exp(x)-x-1). - _Enrique Navarrete_, Apr 15 2022 %e A086443 a(4)=67 since the sequences are the 12 permutations of the form 1000, 2000, 3000; the 18 permutations of the form 1100, 2200, 3300; the 36 permutations of the form 1200, 1300, 2300; and 0000. - _Enrique Navarrete_, Apr 15 2022 %Y A086443 Cf. A000295, A066810. %K A086443 easy,nonn %O A086443 0,4 %A A086443 _Paul Barry_, Jul 21 2003