A385589 - OEIS

%I #8 Jul 07 2025 18:16:36

%S 1,5,22,86,304,992,3040,8864,24832,67328,177664,458240,1159168,

%T 2883584,7069696,17113088,40960000,97058816,227934208,530972672,

%U 1227882496,2820669440,6440353792,14623440896,33034338304,74272735232,166262210560,370675810304,823291543552,1822139875328

%N a(n) = 2^(n-2)*(3*binomial(n,3) + 6*binomial(n,2) + 6*n + 4).

%C 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 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-24,32,-16).

%F E.g.f.: exp(2*x)*(1+x)^3.

%F G.f.: (1 - 3*x + 6*x^2 - 2*x^3)/(1 - 2*x)^4. - _Stefano Spezia_, Jul 03 2025

%e a(1) = 5 since the words are a, b, c, d, e.

%e 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 LinearRecurrence[{8, -24, 32, -16}, {1, 5, 22, 86}, 30] (* _Amiram Eldar_, Jul 03 2025 *)

%Y Cf. A385407.

%K nonn,easy

%O 0,2

%A _Enrique Navarrete_, Jul 03 2025