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A241340
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Number of partitions p of n such that floor(mean(p)) and ceiling(mean(p)) are parts of p.
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5
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0, 1, 2, 3, 4, 5, 7, 8, 11, 15, 18, 22, 37, 36, 50, 73, 89, 100, 152, 161, 249, 290, 330, 413, 646, 666, 803, 1060, 1348, 1473, 2170, 2183, 3003, 3455, 3984, 5318, 6936, 6839, 8494, 10664, 14064, 14322, 19343, 20418, 26417, 32021, 34068, 40921, 56205, 57543
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OFFSET
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0,3
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LINKS
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FORMULA
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EXAMPLE
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a(6) counts these 8 partitions: 6, 33, 321, 3111, 222, 2211, 21111, 111111.
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MATHEMATICA
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z = 30; f[n_] := f[n] = IntegerPartitions[n];
t1 = Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241340 *)
t2 = Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241341 *)
t3 = Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241342 *)
t4 = Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241343 *)
t5 = Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] || MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241344 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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