A007780 Losing initial configurations in 2-hole Tchuka Ruma.

1, 2, 3, 6, 9, 11, 18, 20, 27, 30, 54, 81, 162, 168, 243, 486, 729, 1458, 2187, 4374, 6561, 13122, 19683, 39366, 59049, 118098, 177147, 354294, 531441, 1062882, 1594323, 3188646, 4782969, 9565938, 14348907, 28697814, 43046721, 86093442

Offset

1,2

Comments

The 2-hole Tchuka Ruma game cannot be won for the initial seeds 3^i (i>=1) or 2*3^i (i>=0). Though a sufficient condition, this is not necessary, as can be seen from the terms a(6)=11, a(8)=20, a(10)=30 and a(14)=168. - Pab Ter (pabrlos2(AT)yahoo.com), Nov 08 2005

If any further sporadic term exists, then it exceeds 6973568802. - Sean A. Irvine, Jan 25 2018

Links

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

Paul J. Campbell, and Darrah P. Chavey, Tchuka Ruma Solitaire, The UMAP Journal 16(4) (1995), 343-365.

Formula

Conjectures from Colin Barker, Jan 25 2018: (Start)

G.f.: x*(1 + 2*x - 7*x^5 - 9*x^6 - 13*x^7 - 27*x^8 - 30*x^9 - 27*x^10 - 9*x^11 - 75*x^13 - 243*x^14 - 18*x^15) / (1 - 3*x^2).

a(n) = 3*a(n-2) for n>2.

(End)

Crossrefs

Sequence in context: A176189 A057127 A224449 * A018537 A018331 A032704

Adjacent sequences: A007777 A007778 A007779 * A007781 A007782 A007783

Keyword

nonn

Author

Darrah Chavey

Extensions

More terms from Pab Ter (pabrlos2(AT)yahoo.com), Nov 08 2005

More terms from Sean A. Irvine, Jan 25 2018

Status

approved