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Number of partitions of n into parts that are distinct mod 9.
3

%I #11 Jan 23 2021 16:44:52

%S 1,1,1,2,2,3,4,5,6,8,10,11,15,16,20,25,28,32,39,46,50,62,66,78,93,101,

%T 112,132,150,161,192,202,232,268,287,312,361,400,425,497,516,582,658,

%U 698,748,858,932,982,1135,1164,1296,1443,1519,1610,1845,1968,2059

%N Number of partitions of n into parts that are distinct mod 9.

%H Alois P. Heinz, <a href="/A114098/b114098.txt">Table of n, a(n) for n = 0..2500</a> (terms n = 1..700 from Fausto A. C. Cariboni)

%e a(7)=5 because there are 5 such partition of 7: {7}, {1,6}, {2,5}, {3,4}, {4,2,1}.

%t << DiscreteMath`Combinatorica`; np[n_]:= Length@Select[Mod[ #,9]& /@ Partitions[n],(Length@# != Length@Union@#)&]; lst = Array[np,50]

%K nonn

%O 0,4

%A _Giovanni Resta_, Feb 06 2006

%E a(0)=1 prepended by _Alois P. Heinz_, Jan 23 2021