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A028932 Triangular array of winning positions in Tchoukaillon (or Mancala) solitaire.

%I A028932 #40 Sep 30 2022 08:54:22
%S A028932 0,1,2,0,2,1,3,1,0,3,1,1,4,2,0,0,4,2,0,1,4,2,2,0,4,2,2,1,5,3,1,1,0,5,
%T A028932 3,1,1,1,6,4,2,0,0,0,6,4,2,0,0,1,6,4,2,0,2,0,6,4,2,0,2,1,6,4,2,3,1,0,
%U A028932 6,4,2,3,1,1,7,5,3,1,2,0,0,7,5,3,1,2,0,1
%N A028932 Triangular array of winning positions in Tchoukaillon (or Mancala) solitaire.
%C A028932 The 300 names of Mancala: Abalala'e, Abanga, Abangah, Abouga, Achara, Adi, Adita ta, Adito, Adji, Adjiboto, Adjika, Adji pre, Adjito, Aghi, Agi, Aji, Ajwa, Ale, Andot, Annana, Anywoli, Awale, Awale, Aware, Awari, Awele, Awele Ayo, Ayo Ayo, Azigo,
%C A028932 Ba-Awa, Banga, Bao, Bao kiswahili, Bao solo, Bare, Baruma, Bau, Bawo, Bechi, Boke, Bosh, Bouberoukou, Bouri, Chanka, Chisolo, Chongkak, Choro, Chouba, Chuba, Chunca, Cisolo, Congkak, Coo, Coro, Coro bawo,
%C A028932 Dabuda, dakon, Dakoun, Dara, Darra, Deka, Djonghok, Djonglak, Dwong, erherhe, Endodoi, Enkeshui, Eson xorgol, Esson, eu leu, Fangaya, Fuva, Gabata, Gabatta, Galatjang, Gamacha, Gbegele, Gebta, Gelo, Gepeta, Gesuwa, Gilberta, Giuthi,
%C A028932 Halusa, Hus, Igisoro, Ikiokoto, Imbelece, Imbwe, Impere, Isafu, Ise onzin egbe, Isofu, Isolo, J'erin, jodu, J'odu, Jukuru, Kachig, Ka ia, Kalah, Kalaha, Kalak, Kale, Kalimanta, Kasonko, Katra, Kboo, Kenji guki, Kiarabu, Kisolo, Kiswahilibao, Kiuthi, Kpo, !Krour, Kubuguza,
%C A028932 La'b hakim, La'b madjunni, La'b roseya, Lahemay walida, Lami, Lamlameta, Lamosh, Lam waladach, Langa holo, Layo, leka, Lela, Leyla gobale, Lien, Lizolo, L'ob akila, Lonbeu a cha, Lontu Holo, Luzolo,
%C A028932 Mancala, Mandiare, Manga, Mangala, Mangola, Mankala, Manqala, Manquala, Marabout, Marany, Maruba, Mazageb, Mbangi, Mbau, Mbelete, Mbere, Mbo, Mbothe, Mefuhva, Meusueb, Mewelad, Mofuba, Moro gbegele, Motiq, Msuwa, Mulabalaba, Mungala, Mutiteba, Mwambalula, Mweiso, Mweso,
%C A028932 Nakabile, Nambayi, Naranj, Ncholokoto, Nchomvwa, Nchuba, Nchuwa, Ndoto, Ngar, Njombwa, Nocholokoto, Nsolo, Nsumbi, Ntchuwa, Nummun,
%C A028932 Oko, Olinda, Okwe, Omweeso, Omweso, Otep, Otjitoko, Ot jun, Otra, Ot tjin, Otu, Oure, Ouri, Ourin, Ourre, Ourri, Oware, Owela, Palankuli, Pallamkurie, Pallam kuzhi, Pallanguli, Pallankuli, Pandi, Papadakon, Papandata, Pensur, Pereauni, Peresouni, Poo, Qaluta, Qasuta, Qelat, Ryakati,
%C A028932 Saddeka, Sadeka, Sadiqa, Schach, Serata, Sig, Solo, Sombi, Songo, Soro, Spreta, Sulus ni!shtaw, Sunca, Sungka, Tagega, Tamtam apachi, Tap, Tapata, Tchanka, Tchokajon, Tchonkkak, Tchoukaitlon, Tchukaruma, Tegre, Tjonglak, Toguz xorgol, Toi, Tonka, Topuz xorgol, Tchuba, Tchela, Tshuba, Tshi solo, Tsoro,
%C A028932 Ubao, Ugwasi, Um el bagara, Um el banat, Um el tuweisat, Urdy, Ure, Vai lung thlan, Wale, Walle, Walu, Walya, Ware, Wari, Warri, Wawee, Wawi, Weg, Woaley, Wori, Woribo, Woro, Wouri, Wuli, Wuri, Xorgol, Yada, Yit nuri, Yovodji.
%D A028932 Y. David, On a sequence generated by a sieving process, Riveon Lematematika, 11 (1957), 26-31.
%D A028932 C. Zaslavsky, Africa Counts: Number and Pattern in Traditional African Culture, Boston: Prindle, Weber and Schmidt, 1973.
%H A028932 D. Betten, <a href="http://dx.doi.org/10.1016/S0167-5060(08)70224-3">Kalahari and the Sequence "Sloane No. 377"</a>, Annals Discrete Math., 37, 51-58, 1988.
%H A028932 E. Brisse, <a href="http://members.aol.com/GBShare/awalink.htm">African Games Information and Links</a>
%H A028932 D. M. Broline and _Daniel E. Loeb_, <a href="http://arXiv.org/abs/math.CO/9502225">The combinatorics of Mancala-Type games: Ayo, Tchoukaillon and 1/Pi</a>, J. Undergrad. Math. Applic., vol. 16 (1995), pp. 21-36.
%H A028932 D. Eppstein, <a href="http://www.ics.uci.edu/~eppstein/cgt/">Combinatorial Game Theory</a>
%H A028932 P. Erdős and E. Jabotinsky, <a href="http://dx.doi.org/10.1016/S1385-7258(58)50016-X">On a sequence of integers generated by a sieving process (Part I)</a>, Indagationes Math., 20, 115-123, 1958.
%H A028932 P. Erdős and E. Jabotinsky, <a href="http://dx.doi.org/10.1016/S1385-7258(58)50017-1">On a sequence of integers generated by a sieving process (Part II)</a>, Indagationes Math., 20, 124-128, 1958.
%H A028932 N. J. A. Sloane, <a href="http://neilsloane.com/doc/sg.txt">My favorite integer sequences</a>, in Sequences and their Applications (Proceedings of SETA '98).
%H A028932 R. W. Wilder, <a href="http://dx.doi.org/10.1016/0315-0860(75)90155-X">Review of "Africa Counts: Number and Pattern in Traditional African Culture"</a>, Historia Mathematica, Vol. 2 (1975), pp. 207-210.
%H A028932 C. Zaslavsky, <a href="http://www.math.binghamton.edu/zaslav/cz.html">African and Multicultural Mathematics</a>
%H A028932 <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>
%F A028932 To get the next row in the triangle, find the rightmost zero entry in the current row (which may be to the left of the existing entries). In this zero is in position k (counting from the right), change it from 0 to k and subtract 1 from all the entries to its right.
%e A028932 Triangle begins:
%e A028932 0,
%e A028932 1,
%e A028932 2, 0,
%e A028932 2, 1,
%e A028932 3, 1, 0,
%e A028932 3, 1, 1,
%e A028932 4, 2, 0, 0,
%e A028932 4, 2, 0, 1,
%e A028932 4, 2, 2, 0,
%e A028932 4, 2, 2, 1,
%e A028932 5, 3, 1, 1, 0,
%e A028932 5, 3, 1, 1, 1,
%e A028932 6, 4, 2, 0, 0, 0,
%e A028932 6, 4, 2, 0, 0, 1,
%e A028932 6, 4, 2, 0, 2, 0,
%e A028932 6, 4, 2, 0, 2, 1,
%e A028932 6, 4, 2, 3, 1, 0,
%e A028932 6, 4, 2, 3, 1, 1,
%e A028932 7, 5, 3, 1, 2, 0, 0,
%e A028932 7, 5, 3, 1, 2, 0, 1
%e A028932 ...
%t A028932 s[list_] := Module[{x = Append[list, 0], i = 1}, While[x[[i]] =!= 0, x[[i]] = x[[i]] - 1; i = i + 1]; x[[i]] = i;If[Last@x == 0, Most[x], x]]; Flatten[Reverse /@ NestList[s, {}, 20]] (* _Birkas Gyorgy_, Feb 26 2011 *)
%Y A028932 Cf. A002491, A007952, A028920, A028931, A028933.
%K A028932 nonn,tabf,easy,nice
%O A028932 0,3
%A A028932 _N. J. A. Sloane_
%E A028932 Additional references from _Labos Elemer_, Nov 07 2000
%E A028932 Revised by _N. J. A. Sloane_, Jul 16 2012