

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
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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 (tet12) 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 BizzellBrowning, Apr 27 2019


LINKS

Table of n, a(n) for n=0..29.
Nik BizzellBrowning, Tchoukaillon solitaire sequence, Chromatic pitch table and example.
D. M. Broline and _Daniel E. Loeb_, The combinatorics of MancalaType games: Ayo, Tchoukaillon and 1/Pi, J. Undergrad. Math. Applic., vol. 16 (1995), pp. 2136.


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



