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Number of partitions of n into parts that are distinct mod 8.
2

%I #8 Apr 17 2021 12:58:07

%S 1,1,2,2,3,4,5,6,8,9,12,13,16,20,23,26,31,37,42,47,54,65,72,80,90,108,

%T 115,129,145,168,184,200,220,259,270,301,336,375,411,436,477,546,568,

%U 631,700,755,832,862,945,1050

%N Number of partitions of n into parts that are distinct mod 8.

%H Fausto A. C. Cariboni, <a href="/A114096/b114096.txt">Table of n, a(n) for n = 1..800</a>

%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[ #,8]& /@ Partitions[n],(Length@# != Length@Union@#)&]; lst = Array[np,50]

%t Table[Count[IntegerPartitions[n],_?(Max[Tally[Mod[#,8]][[All,2]]]==1&)],{n,50}] (* _Harvey P. Dale_, Apr 17 2021 *)

%K nonn

%O 1,3

%A _Giovanni Resta_, Feb 06 2006