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Search: id:A161135
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| A161135 |
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Trianular array T(m,n), 1<=n<=m, giving the minimum positive number of deals of m cards into n piles required to collect all cards in the first pile. Each deal tosses all cards from a pile, the last dealt card indicates a pile to deal next, each deal tosses one card consecutively to the 1st, 2nd, ..., nth, 1st, 2nd, ... pile. |
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+0
4
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| 1, 1, 2, 1, 4, 5, 1, 3, 8, 9, 1, 6, 24, 36, 37, 1, 10, 9, 47, 85, 86, 1, 12, 55, 125, 144, 231, 232, 1, 4, 45, 181, 384, 511, 747, 748, 1, 8, 22, 214, 613, 1097, 183, 931, 932, 1, 18, 28, 54, 373, 837, 993, 1931, 2864, 2865, 1, 6, 141, 591, 1642, 3211, 8451, 1836, 14891
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Formatted as a triangular array:
m=1: 1
m=2: 1, 2
m=3: 1, 4, 5
m=4: 1, 3, 8, 9
m=5: 1, 6, 24, 36, 37
m=6: 1, 10, 9, 47, 85, 86
m=7: 1, 12, 55, 125, 144, 231, 232
m=8: 1, 4, 45, 181, 384, 511, 747, 748
m=9: 1, 8, 22, 214, 613, 1097, 183, 931, 932
m=10: 1, 18, 28, 54, 373, 837, 993, 1931, 2864, 2865
m=11: 1, 6, 141, 591, 1642, 3211, 8451, 1836, 14891, 17760, 17761
m=12: 1, 11, 47, 206, 964, 3274, 14079, 14738, 55459, 92010, 109779, 109780
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FORMULA
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T(m,2)=A002326(m-1); T(m,m)=T(m,m-1)+1
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EXAMPLE
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For m=n=3, deals result in a sequence of configurations (listing number of cards in the piles):
3* 0 0
1 1 1*
2* 1 0
1 2* 0
2 1* 0
3* 0 0
where * indicate a pile to deal next. The total number of deals here is T(3,3)=5.
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PROGRAM
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(PARI) { T(m, n) = local(v, r, k, t); v=vector(n); v[1]=m; r=0; k=1; until( vecmax(v)==m, r++; t=v[k]; v[k]=0; k=0; while(t, k++; if(k>n, k=1); v[k]++; t--) ); r }
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CROSSREFS
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A002326 (second column), A161136 (the total number of tossed cards)
Sequence in context: A145861 A129874 A021983 this_sequence A038730 A050166 A124959
Adjacent sequences: A161132 A161133 A161134 this_sequence A161136 A161137 A161138
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KEYWORD
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nonn,tabf
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AUTHOR
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Max Alekseyev (maxale(AT)gmail.com), Jun 02 2009
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