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Search: id:A055941
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| A055941 |
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a(n) = sum( i[j] - j, j = 0 .. k-1) where n = sum( 2^i[j], j = 0 .. k-1). |
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+0
1
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| 0, 0, 1, 0, 2, 1, 2, 0, 3, 2, 3, 1, 4, 2, 3, 0, 4, 3, 4, 2, 5, 3, 4, 1, 6, 4, 5, 2, 6, 3, 4, 0, 5, 4, 5, 3, 6, 4, 5, 2, 7, 5, 6, 3, 7, 4, 5, 1, 8, 6, 7, 4, 8, 5, 6, 2, 9, 6, 7, 3, 8, 4, 5, 0
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Used to calculate number of subspaces of Zp^n where Zp is field of integers mod p.
Consider a square matrix A, and call it special if (0) A is an upper triangular matrix, (1) a nonzero column of A has a 1 on the main diagonal, and (2) if a row has a 1 on the main diagonal then this is the only nonzero element in that row.
If the diagonal of a special matrix is given (it can only contain 0's and 1's), many of the fields of A are determined by (0), (1) and (2). The number of fields that can be freely chosen while still satisfying (0), (1) and (2) is a(n), where n is the diagonal, read as a binary number with least significant bit at upper left.
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REFERENCES
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A. Siegel, Linear Aspects of Boolean Functions, 1999 (unpublished)
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EXAMPLE
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20 = 2^4 + 2^2, thus a(20) = (2-0) + (4-1) = 5
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CROSSREFS
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Adjacent sequences: A055938 A055939 A055940 this_sequence A055942 A055943 A055944
Sequence in context: A081733 A102587 A119387 this_sequence A068076 A138498 A050319
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KEYWORD
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nonn
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AUTHOR
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Anno Siegel (siegel(AT)zrz.tu-berlin.de), Jul 18 2000
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