A153340 Number of zig-zag paths from top to bottom of a rectangle of width 8 with n rows

8, 14, 26, 48, 90, 168, 316, 592, 1114, 2090, 3932, 7382, 13884, 26076, 49032, 92110, 173170, 325360, 611618, 1149248, 2160212, 4059360, 7629882, 14338290, 26949004, 50644750, 95185300, 178883252, 336200648, 631835054, 1187485194, 2231705808