A324275 Numbers k for which A324274(k) is 0, i.e., starting squares in A324274 that yield a path of infinite length.

2, 9, 14, 27, 34, 53, 64, 89, 102, 133, 150, 187, 206, 249, 272, 321, 346, 401, 430, 491, 522, 589, 624, 697, 734, 813, 854, 939, 982, 1073, 1120, 1217, 1266, 1369, 1422, 1531, 1586, 1701, 1760, 1881, 1942, 2069, 2134, 2267, 2334, 2473

Offset: 1

Author

Jan Koornstra, Feb 27 2019

Keywords

• nonn

Comments

Note that the sequence up to a(n) (for its current known values) is actually the path of a(n) in reverse until it reaches square 2. It is therefore conjectured that all starting squares in A324274 either have a finite length or are part of this single sequence.

Crossrefs

Cf. A316588, A324273, A324274.

Formula

Conjectures from Colin Barker, Mar 09 2019: (Start)

G.f.: x*(2 + 7*x + 3*x^2 + 6*x^3 - x^5 + x^6) / ((1 - x)^3*(1 + x)^2*(1 + x^2)).

a(n) = (5 + 7*(-1)^n + (2-2*i)*(-i)^n + (2+2*i)*i^n + (26+6*(-1)^n)*n + 18*n^2) / 16 where i=sqrt(-1).

a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-4) - a(n-5) - a(n-6) + a(n-7) for n>7.

(End)