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A035537
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Number of partitions of n with equal nonzero number of parts congruent to each of 0 and 1 (mod 3).
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0
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0, 0, 0, 0, 1, 0, 1, 2, 2, 3, 5, 5, 9, 10, 15, 18, 24, 30, 40, 47, 65, 76, 97, 120, 150, 179, 229, 270, 336, 404, 494, 588, 722, 852, 1035, 1227, 1476, 1744, 2090, 2461, 2935, 3446, 4092, 4795, 5665, 6627, 7801, 9096, 10680, 12426, 14528, 16881, 19680, 22800, 26525
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OFFSET
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0,8
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LINKS
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MAPLE
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b := proc(n, i, t, s) option remember; `if`(n=0,
`if`(t = s and t >= 1, 1, 0), `if`(i<1, 0, b(n, i-1, t, s)+
b(n-i, min(n-i, i), t + [1, 0, 0][1+irem(i, 3)], s + [0, 1, 0][1+irem(i, 3)])))
end:
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MATHEMATICA
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equalQ[partit_] := With[{t = Total[Switch[Mod[#, 3], 0, {1, 0, 0}, 1, {0, 1, 0}, 2, {0, 0, 1}]& /@ partit]}, t[[1]] > 0 && t[[1]] == t[[2]]]; a[n_] := Select[IntegerPartitions[n], equalQ] // Length; a[0] = 0; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 54}] (* Jean-François Alcover, Dec 07 2016 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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