お題　何通り？
黒玉 b 個、赤玉 r 個、白玉 w 個が入ってる袋の中から玉を一個ずつ取り出し、取り出した玉を順に横一列に b+r+w 個すべて並べる。

どの黒玉同士も隣り合わず、どの赤玉同士も隣り合わない数を求めよ

例　
( b, r, w ) = ( 1,2,2)
→ 18
( b, r, w ) = ( 1,2,3 )
→ 40
( b, r, w ) = ( 3,4,5 )
→ 4326
( b, r, w ) = ( 12,34,56 )
→ 138961718287080638152811314224672

( b, r, w ) = ( 1, 2, 2 )の場合の18通り
["BRWRW","BRWWR","BWRWR","RBRWW","RBWRW","RBWWR","RWBRW","RWBWR","RWRBW","RWRWB","RWWBR","RWWRB","WBRWR","WRBRW","WRBWR","WRWBR","WRWRB","WWRBR"]