A106637 - OEIS

%I #8 Oct 02 2023 23:30:48

%S 2,3,5,8,11,13,14,15,17,20,21,23,26,29,31,32,33,35,38,39,41,44,47,49,

%T 50,51,53,56,57,59,62,65,67,68,69,71,74,75,77,80,83,85,86,87,89,92,93,

%U 95,98,101,103,104,105,107,110,111,113,116,119,121,122,123,125,128,129,131

%N Accumulation of permutation sequence on three symbols such that a(n+2) - 2*a(n+1) - a(n) = 0 overall.

%C The sequence simulated: cc = Table[N[(Pi/2)*(b[n] + 7)], {n, 1, 3*digits}] behaves a lot like the rational approximation of the zeta zeros.

%F f[n] from either {2, 1, 0} or {0, 1, 2} a(n) = a(n-1) + 1+f[n]

%F Empirical g.f.: x*(x^9+2*x^8+x^7+x^6+2*x^5+3*x^4+3*x^3+2*x^2+x+2) / ((x-1)^2*(x^2+x+1)*(x^6+x^3+1)). [_Colin Barker_, Dec 02 2012]

%t digits = 67 f = Flatten[Table[If[Mod[n, 2] == 0, {2, 1, 0}, {0, 1, 2}], {n, 1, digits}]] b[1] = 2; b[n_] := b[n] = b[n - 1] + 1 + f[[n]] aa = Table[b[n], {n, 1, 3*digits}]

%K nonn,uned

%O 1,1

%A _Roger L. Bagula_, May 11 2005