In how many ways you can build a tower of height n, using 1X3, 2X3, and 3X3 blocks. \n[ ][ ][ ]\n[ ][ ][ ]\t[ ][ ][ ]\n[ ][ ][ ]\t[ ][ ][ ]  [ ][ ][ ]\n\nYou can use any number of blocks, and rotations are counted as different. \n\nExamples: \n\n- n=1 : only way we can build a tower of height 1 and width 3 is by picking 1 1X3 matrix.  \n\n- n=2 : 2 ways, i.e chose 2 blocks of 1X3 or 1 block of 2X3.  \n\n- rotation don\'t really count as they\'d be the same orientaion in the above base cases.\n\n- n=3 : 6 ways \n \n Let\'s say 000 -1X3\'s and xxx represents 2X3\'s and Y\'s represents 3X3 so we have following ways:\n \n000  XXX  000  0XX XX0  YYY\n000  XXX  XXX  0XX XX0  YYY \n000  000  XXX  0XX XX0  YYY\n\nInterviewer helped me to find the combinations for n=3 in interview I counted 7, and he agreed :|, which if I think now is wrong since the case below wouldn\'t be valid:\nXXX\n000\nXXX  \n

In how many ways you can build a tower of height n, using 1X3, 2X3, and 3X3 blocks. \n[ ][ ][ ]\n[ ][ ][ ]\t[ ][ ][ ]\n[ ][ ][ ]\t[ ][ ][ ]  [ ][ ][ ]\n\nYou ca