A106637 Accumulation of permutation sequence on three symbols such that a(n+2) - 2*a(n+1) - a(n) = 0 overall.

2, 3, 5, 8, 11, 13, 14, 15, 17, 20, 21, 23, 26, 29, 31, 32, 33, 35, 38, 39, 41, 44, 47, 49, 50, 51, 53, 56, 57, 59, 62, 65, 67, 68, 69, 71, 74, 75, 77, 80, 83, 85, 86, 87, 89, 92, 93, 95, 98, 101, 103, 104, 105, 107, 110, 111, 113, 116, 119, 121, 122, 123, 125, 128, 129, 131

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..66.

Formula

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

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]

Mathematica

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}]

Crossrefs

Sequence in context: A298120 A298205 A117725 * A246361 A228855 A171048

Adjacent sequences: A106634 A106635 A106636 * A106638 A106639 A106640

Keyword

nonn,uned

Author

Roger L. Bagula, May 11 2005

Status

approved