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Search: id:A086885
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| A086885 |
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Lower triangular matrix, read by rows: T(i,j) = number of ways i seats can be occupied by any number k (0<=k<=j<=i) of persons. |
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+0
6
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| 2, 3, 7, 4, 13, 34, 5, 21, 73, 209, 6, 31, 136, 501, 1546, 7, 43, 229, 1045, 4051, 13327, 8, 57, 358, 1961, 9276, 37633, 130922, 9, 73, 529, 3393, 19081, 93289, 394353, 1441729, 10, 91, 748, 5509, 36046, 207775, 1047376, 4596553, 17572114, 11, 111, 1021, 8501
(list; table; graph; listen)
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OFFSET
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1,1
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COMMENT
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2
3 7
4 13 34
5 21 73 209
6 31 136 501 1546
Compare with A088699. [From Peter Bala (pbala(AT)toucansurf.com), Sep 17 2008]
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LINKS
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Ed Jones, Number of seatings
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FORMULA
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a(n)=T(i, j) with n=(i*(i-1))/2+j; T(i, 1)=i+1, T(i, j)=T(i, j-1)+i*T(i-1, j-1) for j>1
The role of seats and persons may be interchanged, so T(i, j)=T(j, i).
T(i, j) = j!*LaguerreL(j, i-j, -1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 25 2003
T(i, j) = Sum_{k=0..j} k!*binomial(i, k)*binomial(j, k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 25 2003
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EXAMPLE
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One person:
T(1,1)=a(1)=2: 0,1 (seat empty or occupied)
T(2,1)=a(2)=3: 00,10,01 (both seats empty, left seat occupied, right seat occupied)
Two persons:
T(2,2)=a(3)=7: 00,10,01,20,02,12,21
T(3,2)=a(5)=13: 000,100,010,001,200,020,002,120,102,012,210,201,021
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CROSSREFS
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Diagonal: A002720, first subdiagonal: A000262, 2nd subdiagonal: A052852, 3rd subdiagonal: A062147, 4th subdiagonal: A062266, 5th subdiagonal: A062192, 2nd row/column: A002061.
Sequence in context: A143528 A118810 A026259 this_sequence A082734 A021425 A060940
Adjacent sequences: A086882 A086883 A086884 this_sequence A086886 A086887 A086888
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KEYWORD
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nonn,tabl
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Aug 22 2003
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