A251340Number of (n+1)X(5+1) 0..3 arrays with every 2X2 subblock summing to a nonzero multiple of 3.

72375, 1487375, 36988354, 1151715397, 43807665267, 1921884757552, 91970680872031, 4623720852303067, 238904752638164194, 12533399410057395845, 663156544051782139723, 35257699651874025415400, 1879661570818351400907467

The first term appear at position 47,232.

…63243191000223929785255372375566213644740096760539439…
position 47,232
termsstringfirst positionoccurrences
17237547,23210,106
2723751487375not within 1,000,000,0000

Searched the first 1,000,000,000 digits. Strings longer than 12 digits are not indexed.