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A118670 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). 0
2, 5, 14, 19, 17, 181, 119, 17, 2459, 121, 89, 181, 545, 59 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=1..14.


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.


Cf. A118141.

Sequence in context: A131356 A191119 A089410 * A228958 A216669 A015633

Adjacent sequences:  A118667 A118668 A118669 * A118671 A118672 A118673




John W. Layman, May 19 2006



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Last modified July 13 15:18 EDT 2020. Contains 335688 sequences. (Running on oeis4.)