A028931 Strings giving winning positions in Tchoukaillon (or Mancala) solitaire.

0, 1, 20, 21, 310, 311, 4200, 4201, 4220, 4221, 53110, 53111, 642000, 642001, 642020, 642021, 642310, 642311, 7531200, 7531201, 7531220, 7531221, 86420110, 86420111, 86424000, 86424001, 86424020, 86424021, 86424310, 86424311

Offset

0,3

Comments

a(n) gives string listing winning position for n stones.

Sum of numbers in a(n) is equal to n.

Using the chromatic (tet-12) scale, (if C=0, 12, 24...) all integers correspond to pitches C, C#, G#, A, Bb, B, a recursive pattern that evenly bisects the octave and avoids the tritone (IC6). - Nik Bizzell-Browning, Apr 27 2019

Links

Table of n, a(n) for n=0..29.

Nik Bizzell-Browning, Tchoukaillon solitaire sequence, Chromatic pitch table and example.

Nicholas John Bizzell-Browning, LIE scales: Composing with scales of linear intervallic expansion, Ph. D. Thesis, Brunel Univ. (UK, 2024). See p. 142.

D. M. Broline and Daniel E. Loeb, The combinatorics of Mancala-Type games: Ayo, Tchoukaillon and 1/Pi, J. Undergrad. Math. Applic., vol. 16 (1995), pp. 21-36.

Formula

To get the next term, if rightmost 0 is in position i, replace it by i and subtract 1 from all earlier entries.

Example

For example, a(10) = 53111; rightmost 0 is in position 6, so get 653111 -> a(11) = 642000.

Crossrefs

Cf. A002491, A007952, A028920, A028932, A028933.

Sequence in context: A041834 A219798 A063013 * A063012 A302205 A041836

Adjacent sequences: A028928 A028929 A028930 * A028932 A028933 A028934

Keyword

nonn,nice,easy,base

Author

N. J. A. Sloane

Extensions

More terms from Erich Friedman

Status

approved