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A161135 Triangular 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 first, 2nd, ..., n-th, first, 2nd, ... pile. 3
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; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
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
LINKS
FORMULA
T(m,2)=A002326(m-1); T(m,m)=T(m,m-1)+1
EXAMPLE
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.
PROG
(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 }
CROSSREFS
A002326 (second column), A161136 (the total number of tossed cards)
Sequence in context: A021983 A349994 A194363 * A237274 A038730 A188106
KEYWORD
nonn,tabf
AUTHOR
Max Alekseyev, Jun 02 2009
STATUS
approved

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Last modified June 18 16:37 EDT 2024. Contains 373482 sequences. (Running on oeis4.)