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 A143100 #9 Feb 06 2019 01:57:37 %S A143100 1,3,4,6,13,30,64,129,256,510,1021,2046,4096,8193,16384,32766,65533, %T A143100 131070,262144,524289,1048576,2097150,4194301,8388606,16777216, %U A143100 33554433,67108864,134217726,268435453,536870910,1073741824,2147483649,4294967296,8589934590 %N A143100 A007318 * A143098. %H A143100 Nathaniel Johnston, <a href="/A143100/b143100.txt">Table of n, a(n) for n = 1..500</a> %F A143100 Binomial transform of A143098: (1, 2, -1, 2, 2, -1, 2, 2, -1, 2, 2, ...). %F A143100 From _R. J. Mathar_, Jul 31 2008: (Start) %F A143100 G.f.: (3x^3 - 2x^2 - x + 1)*x/((x^2-x+1)*(2x-1)*(x-1)). %F A143100 a(n) = -1 + 2^(n-1) + A057079(n-1). (End) %e A143100 a(4) = 6 = (1, 3, 3, 1) dot (1, 2, -1, 2) = (1 + 6 - 3 + 2). %p A143100 A143098 := proc(n) if(n=1)then return 1: elif(n mod 3 = 0)then return -1: else return 2: fi: end: A143100 := proc(n) return add(binomial(n-1,k-1)*A143098(k),k=1..n): end: seq(A143100(n),n=1..34); # _Nathaniel Johnston_, Apr 30 2011 %Y A143100 Cf. A143097, A143098, A143099. %K A143100 nonn %O A143100 1,2 %A A143100 _Gary W. Adamson_, Jul 24 2008