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Search: id:A118670
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| A118670 |
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Length of the shortest perfect modular pattern of type PMP(3,0) of n columns whose first row is 0...01 (with n-1 zeros). |
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+0
1
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| 2, 5, 14, 19, 17, 181, 119, 17, 2459, 121, 89, 181, 545, 59
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OFFSET
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1,1
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COMMENT
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A modular pattern of type PMP(m,r) is a matrix of integers in the range 0 to (r-1) with the property that the sum of any element and its four adjacent elements is congruent to r (modulo m). The pattern is called perfect if no row or column is entirely zero. This generalizes the concept of perfect parity pattern introduced by D. E. Knuth in A118141. a(15) is greater than 4800.
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EXAMPLE
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For 2 columns (n=2), if we start with the first row 0 1, it is found that successive additional rows such that the currently last row satisfies the PMP(3,0) condition
are uniquely determined. This leads, after several steps, to
0 1
2 2
2 1
1 1
2 0
Since, for the first time, the last (5th) row also satisfies the condition, we have found that the shortest PMP(3,0) matrix of 2 columns has 5 rows, and thus a(2)=5.
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CROSSREFS
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Cf. A118141.
Sequence in context: A137271 A131356 A089410 this_sequence A015633 A131661 A076664
Adjacent sequences: A118667 A118668 A118669 this_sequence A118671 A118672 A118673
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), May 19 2006
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