A301844Number of 4Xn 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

8, 128, 773, 5748, 39703, 281758, 1986213, 14047365, 99396932, 703490647, 4979239708, 35242914039, 249447707376, 1765580587312, 12496708381182, 88451201375638, …

The first term appear at position 11.

14159265358979323846264338327950288…
position 11
termsstringfirst positionoccurrences
1811100,001,839
2812814799,813
3812877313,085,462100
481287735748not within 1,000,000,0000

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