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 A385589 #8 Jul 07 2025 18:16:36
%S A385589 1,5,22,86,304,992,3040,8864,24832,67328,177664,458240,1159168,
%T A385589 2883584,7069696,17113088,40960000,97058816,227934208,530972672,
%U A385589 1227882496,2820669440,6440353792,14623440896,33034338304,74272735232,166262210560,370675810304,823291543552,1822139875328
%N A385589 a(n) = 2^(n-2)*(3*binomial(n,3) + 6*binomial(n,2) + 6*n + 4).
%C A385589 a(n) is the number of words of length n defined on 5 letters that contain zero or one a's, zero or one b's, zero or one c's, and any number of d's and e's.
%H A385589 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-24,32,-16).
%F A385589 E.g.f.: exp(2*x)*(1+x)^3.
%F A385589 G.f.: (1 - 3*x + 6*x^2 - 2*x^3)/(1 - 2*x)^4. - _Stefano Spezia_, Jul 03 2025
%e A385589 a(1) = 5 since the words are a, b, c, d, e.
%e A385589 a(2) = 22 since the words are ab, ba, ac, ca, ad, da, ae, ea, bc, cb, bd, db, be, eb, cd, dc, ce, ec, de, ed, dd, ee.
%t A385589 LinearRecurrence[{8, -24, 32, -16}, {1, 5, 22, 86}, 30] (* _Amiram Eldar_, Jul 03 2025 *)
%Y A385589 Cf. A385407.
%K A385589 nonn,easy
%O A385589 0,2
%A A385589 _Enrique Navarrete_, Jul 03 2025