a(n) is the number of patterns for n-digit papaya numbers.

Terms

a(0) =1a(1) =2a(2) =4a(3) =10a(4) =21a(5) =50a(6) =99a(7) =250a(8) =454a(9) =1242a(10) =2223a(11) =6394a(12) =11389a(13) =35002a(14) =62034a(15) =202010a(16) =359483a(17) =1233518a(18) =2203507a(19) =7944100a(20) =14249715a(21) =53810836a(22) =96911168a(23) =382258438a(24) =691048071a(25) =2840120987a(26) =5152403569a(27) =22010733048a(28) =40059670261a(29) =177444599715