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).

2, 5, 14, 19, 17, 181, 119, 17, 2459, 121, 89, 181, 545, 59

Offset: 1

Author

John W. Layman, May 19 2006

Keywords

• nonn

Comments

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.

Examples

			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.
		

Crossrefs

Cf. A118141.