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

1,1

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.

Links

Table of n, a(n) for n=1..46.

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)

Crossrefs

Cf. A316588, A324273, A324274.

Sequence in context: A224855 A366938 A254608 * A106360 A024470 A024472

Adjacent sequences: A324272 A324273 A324274 * A324276 A324277 A324278

Keyword

nonn

Author

Jan Koornstra, Feb 27 2019

Status

approved