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 A383608 #9 May 03 2025 10:03:09 %S A383608 1,1,2,6,8,40,32,224,128,1152,512,5632,2048,26624,8192,122880,32768, %T A383608 557056,131072,2490368,524288,11010048,2097152,48234496,8388608, %U A383608 209715200,33554432,905969664,134217728,3892314112,536870912,16642998272,2147483648,70866960384,8589934592 %N A383608 Expansion of e.g.f. (1+x)*cosh(x)^2. %C A383608 a(n) is the number of ternary strings of length n with an even number of 0s and 2s and one or no 1s. %C A383608 A081294 and A229580 interleaved. %H A383608 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,8,0,-16). %F A383608 a(n)=2^(n-1) for n even, n > 0, a(0)=1. %F A383608 a(n)=n*2^(n-2) for n odd, n > 1, a(1)=1. %F A383608 G.f.: (1 + x - 6*x^2 - 2*x^3 + 8*x^4 + 8*x^5)/(1 - 4*x^2)^2. - _Stefano Spezia_, May 02 2025 %F A383608 a(n) = 8*a(n-2) - 16*a(n-4), n > 5. %e A383608 a(5)=40 since the strings are the 30 permutations of 00221, the 5 permutations of 00001, and the 5 permutations of 22221. %Y A383608 Cf. A081294, A229580. %K A383608 nonn,easy %O A383608 0,3 %A A383608 _Enrique Navarrete_, May 01 2025