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Search: id:A129312
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| A129312 |
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A minimal 2 X 2 subdeterminant array. |
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+0
1
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| 1, 2, 2, 3, 5, 3, 4, 8, 8, 4, 5, 11, 13, 11, 5, 6, 14, 18, 18, 14, 6, 7, 17, 23, 25, 23, 17, 7, 8, 20, 28, 32, 32, 28, 20, 8, 9, 23, 33, 39, 41, 39, 33, 23, 9, 10, 26, 38, 46, 50, 50, 46, 38, 26, 10, 11, 29, 43, 53, 59, 61, 59, 53, 43, 29, 11, 12, 32, 48, 60, 68, 72, 72, 68, 60
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Given that row 1 and column 1 are the sequence (1,2,3,4,...), T is the array of minimal positive subdeterminants in the sense that for each 2 X 2 submatrix
a b
c d,
d is the least integer for which the resulting
determinant is positive; indeed, the determinant is 1.
T(n,n)=A001844(n).
SUM{T(n,k): k=1,2,...,n}=A081436(n).
When T is written as the triangle
1
2 2
3 5 3
4 8 8 4
5 11 13 11 5, etc.,
the row sums are A006527 and the alternating row sums are 1,0,1,0,1,0,1,0,... (A059841).
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FORMULA
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T(n,k)=(2n-1)*k-n+1.
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EXAMPLE
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Northwest corner:
1 2 3 4 5 6
2 5 8 11 14 17
3 8 13 18 23 28
4 11 18 25 32 39
T(2,2)=5 because 5 is the least positive integer x for which the determinant of the 2 X 2 matrix below is positive:
1 2
2 x
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CROSSREFS
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Cf. A001844, A081436, A006527, A059841.
Sequence in context: A131901 A132071 A061177 this_sequence A115262 A128141 A014430
Adjacent sequences: A129309 A129310 A129311 this_sequence A129313 A129314 A129315
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Apr 09 2007
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