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 A066345 #14 Jun 13 2015 00:50:30 %S A066345 1,1,4,7,20,39,96,191,432,863,1856,3711,7744,15487,31744,63487,128768, %T A066345 257535,519168,1038335,2085888,4171775,8364032,16728063,33501184, %U A066345 67002367,134103040,268206079,536625152,1073250303,2146959360 %N A066345 Winning binary "same game" templates of length n as defined below. %C A066345 A "same game template" is a pattern representing the run pattern of a string in a 2 symbol alphabet. Each position in the template represents either an isolated symbol, or a run of two or more identical symbols. Such a template can be represented as a ternary number without digit 0 (A007931), where 2 represents any run of 2 or more identical symbols and ternary 1 represents remaining single bitsymbols, e.g. 211 for 0010, 1101, 00010, etc. A winning template represents an infinite subset of winning binary "same games", e.g. 121 for 0110, 1001, 01110, etc. %H A066345 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2,5,-10,-8,16,4,-8). %F A066345 a(2*n-1)= 2^(2*n-1) -n * 2^(n-1), a(2*n)= 2*a(2*n-1) -1. %F A066345 G.f. x*( 1-x-3*x^2+4*x^3+4*x^4-4*x^5 ) / ( (x-1)*(2*x-1)*(1+x)*(-1+2*x^2)^2 ). - _R. J. Mathar_, May 07 2013 %e A066345 There are a(3)= 4 winning templates 121, 122, 221, 222 with 3 ternary digits and a(4)= 7 winning templates 1212, 2121, 1222, 2221, 2122, 2212, 2222. %Y A066345 a(2*n-1)= A008353(n-1), cf. A035615, A007931, A066067. %K A066345 nonn,easy %O A066345 1,3 %A A066345 _Frank Ellermann_, Dec 23 2001