login
This site is supported by donations to The OEIS Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A028932 Triangular array of winning positions in Tchoukaillon (or Mancala) solitaire. 6
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, 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, 6, 4, 2, 3, 1, 1, 7, 5, 3, 1, 2, 0, 0, 7, 5, 3, 1, 2, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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,

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,

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,

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,

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,

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,

Nakabile, Nambayi, Naranj, Ncholokoto, Nchomvwa, Nchuba, Nchuwa, Ndoto, Ngar, Njombwa, Nocholokoto, Nsolo, Nsumbi, Ntchuwa, Nummun,

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,

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,

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.

REFERENCES

Y. David, On a sequence generated by a sieving process, Riveon Lematematika, 11 (1957), 26-31.

C. Zaslavsky, Africa Counts: Number and Pattern in Traditional African Culture, Boston: Prindle, Weber and Schmidt, 1973.

LINKS

Table of n, a(n) for n=0..87.

D. Betten, Kalahari and the Sequence "Sloane No. 377", Annals Discrete Math., 37, 51-58, 1988.

E. Brisse, African Games Information and Links

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.

D. Eppstein, Combinatorial Game Theory

P. Erdős and E. Jabotinsky, On a sequence of integers generated by a sieving process (Part I), Indagationes Math., 20, 115-123, 1958.

P. Erdős and E. Jabotinsky, On a sequence of integers generated by a sieving process (Part II), Indagationes Math., 20, 124-128, 1958.

N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).

R. W. Wilder, Review of "Africa Counts: Number and Pattern in Traditional African Culture", Historia Mathematica, Vol. 2 (1975), pp. 207-210.

C. Zaslavsky, African and Multicultural Mathematics

Index entries for sequences generated by sieves

FORMULA

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.

EXAMPLE

Triangle begins:

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, 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,

6, 4, 2, 3, 1, 1,

7, 5, 3, 1, 2, 0, 0,

7, 5, 3, 1, 2, 0, 1

...

MATHEMATICA

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 *)

CROSSREFS

Cf. A002491, A007952, A028920, A028931, A028932, A028933.

Sequence in context: A082023 A078152 A191247 * A076473 A163160 A237184

Adjacent sequences:  A028929 A028930 A028931 * A028933 A028934 A028935

KEYWORD

nonn,tabf,easy,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

Additional references from Labos Elemer, Nov 07 2000

Revised by N. J. A. Sloane, Jul 16 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 18 06:34 EST 2019. Contains 319269 sequences. (Running on oeis4.)