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

Author

Darrah Chavey

Keywords

• nonn

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)

Extensions

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

More terms from Sean A. Irvine, Jan 25 2018