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 A385083 #9 Jun 19 2025 00:13:14 %S A385083 0,1,1,3,6,5,15,7,28,9,45,11,66,13,91,15,120,17,153,19,190,21,231,23, %T A385083 276,25,325,27,378,29,435,31,496,33,561,35,630,37,703,39,780,41,861, %U A385083 43,946,45,1035,47,1128,49,1225,51,1326,53,1431,55,1540,57,1653,59,1770 %N A385083 Expansion of e.g.f. cosh(x)*(x + x^2/2). %C A385083 Hexagonal numbers and odd numbers interleaved. %C A385083 a(n) is the number of ternary strings of length n that contain exactly one 0 and no 1's or exactly two 1's and no 0's, and in both cases, an even number of 2's. %H A385083 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-3,0,1). %F A385083 a(n) = (n/2)*(n-1), n even; a(n) = n, n odd. %F A385083 G.f.: x*(1 + x + 3*x^3 - x^4)/(1 - x^2)^3. - _Stefano Spezia_, Jun 17 2025 %e A385083 a(7) = 7 since the strings are the 7 permutations of 0222222. %e A385083 a(8) = 28 since the strings are the 28 permutations of 11222222. %Y A385083 Cf. A000384, A005408. %K A385083 nonn,easy %O A385083 0,4 %A A385083 _Enrique Navarrete_, Jun 17 2025