A241552 - OEIS

%I #4 May 03 2014 16:53:23

%S 0,0,0,0,1,1,2,3,5,8,12,17,23,34,47,64,87,115,154,204,266,346,444,573,

%T 731,933,1174,1479,1855,2320,2884,3578,4411,5443,6678,8185,9977,12157,

%U 14753,17886,21608,26058,31326,37631,45066,53911,64300,76609,91061

%N Number of partitions p of n such that (number of numbers of the form 5k + 3 in p) is a part of p.

%C Each number in p is counted once, regardless of its multiplicity.

%e a(6) counts these 2 partitions:  321, 3111.

%t z = 30; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 5], k]

%t Table[Count[f[n], p_ /; MemberQ[p, s[0, p]]], {n, 0, z}]  (* A241549 *)

%t Table[Count[f[n], p_ /; MemberQ[p, s[1, p]]], {n, 0, z}]  (* A241550 *)

%t Table[Count[f[n], p_ /; MemberQ[p, s[2, p]]], {n, 0, z}]  (* A241551 *)

%t Table[Count[f[n], p_ /; MemberQ[p, s[3, p]]], {n, 0, z}]  (* A241552 *)

%t Table[Count[f[n], p_ /; MemberQ[p, s[4, p]]], {n, 0, z}]  (* A241553 *)

%Y Cf. A241549, A241550, A241551, A241553.

%K nonn,easy

%O 0,7

%A _Clark Kimberling_, Apr 26 2014