A164148 Number of binary strings of length n with equal numbers of 0000 and 0010 substrings

1, 2, 4, 8, 14, 25, 46, 86, 160, 294, 545, 1016, 1904, 3565, 6686, 12585, 23770, 45013, 85392, 162393, 309621, 591792, 1133516, 2175532, 4184036, 8062871, 15566675, 30105898, 58320830, 113156619, 219878845, 427850213, 833616314, 1626199001