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A028931 Strings giving winning positions in Tchoukaillon (or Mancala) solitaire. 5
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 (list; graph; refs; listen; history; text; internal format)
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.

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

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Last modified December 6 08:36 EST 2022. Contains 358605 sequences. (Running on oeis4.)