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05AB1E, 17 bytes

" "Ç©IED®âO«]I¢

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Explanation

" " String containing code points for 6, 9, and 20
 Ç Convert code points to integer list to get [6, 9, 20]
 © Store this list in register_c
 IE Loop <input> number of times
 ®â Cartesian product stack contents with list in register_c
 O Sum up the contents of each sub array
 D « List duplicated before taking Cartesian product, concat
 ] End for loop
 I¢ Count occurences of input

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