A161136 -id:A161136 - cp's OEIS frontend

A161138 Main diagonal of the triangular array A161136.

Original entry on oeis.org

1, 3, 9, 18, 80, 196, 554, 1824, 2292, 7218, 45522, 288135, 660113, 3201130, 10512530, 17675063, 191230544, 207521990

Offset: 1

Max Alekseyev, Jun 02 2009

Cf. A161135, A161136, A161137.

a(m) = A161136(m,m).

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.

Original entry on oeis.org

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

Offset: 1

Max Alekseyev, Jun 02 2009

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

			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.

A002326 (second column), A161136 (the total number of tossed cards)

{ 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 }

T(m,2)=A002326(m-1); T(m,m)=T(m,m-1)+1

A161137 Main diagonal of the triangular array A161135.

Original entry on oeis.org

1, 2, 5, 9, 37, 86, 232, 748, 932, 2865, 17761, 109780, 249840, 1190787, 3869645, 6479631, 69445201, 75334942

Offset: 1

Max Alekseyev, Jun 02 2009

A161135, A161136, A161138

a(m) = A161135(m,m)

cp's OEIS Frontend

A161138 Main diagonal of the triangular array A161136.

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A161137 Main diagonal of the triangular array A161135.

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