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A028931
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Strings giving winning positions in Tchoukaillon (or Mancala) solitaire.
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6
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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
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OFFSET
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0,3
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COMMENTS
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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
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LINKS
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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.
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FORMULA
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To get the next term, if rightmost 0 is in position i, replace it by i and subtract 1 from all earlier entries.
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EXAMPLE
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For example, a(10) = 53111; rightmost 0 is in position 6, so get 653111 -> a(11) = 642000.
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CROSSREFS
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Cf. A002491, A007952, A028920, A028931, A028932, A028933.
Sequence in context: A041834 A219798 A063013 * A063012 A302205 A041836
Adjacent sequences: A028928 A028929 A028930 * A028932 A028933 A028934
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KEYWORD
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nonn,nice,easy,base
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Erich Friedman
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STATUS
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approved
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