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 A299408 Number of partitions of n whose minimal excluded multiplicity is even. 1
 0, 1, 1, 2, 2, 4, 6, 9, 11, 17, 24, 33, 41, 59, 75, 99, 128, 168, 214, 278, 347, 438, 559, 696, 866, 1084, 1346, 1653, 2044, 2500, 3070, 3741, 4559, 5507, 6712, 8061, 9746, 11699, 14076, 16794, 20141, 23943, 28588, 33904, 40291, 47593, 56461, 66462, 78495 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS This is analogous to the minimal excludant of Fraenkel. LINKS A. S. Fraenkel, U. Peled, Harnessing the Unwieldy MEX Function, In: Games of No Chance 4, Proc. BIRS Workshop on Combinatorial Games, 2008, Banff, Alberta, Canada, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 63, Cambridge University Press, Cambridge, 77-94, 2015. FORMULA a(n) = A000041(n) - A300183(n). EXAMPLE For the partition 1+1+2; 2 has multiplicity 1; 1 has multiplicity 2, so the smallest absent multiplicity is 3, which is odd. So this partition is not counted. a(4) = 2: [3,1], [4]. a(5) = 4: [2,1,1,1], [3,2], [4,1], [5]. a(6) = 6: [2,1,1,1,1], [3,1,1,1], [3,2,1], [4,2], [5,1], [6]. MATHEMATICA << Combinatorica`; nend = 15; For[n = 1, n <= nend, n++, count[n] = 0;   For[i = 1, i <= PartitionsP[n], i++, partition = Partitions[n][[i]];     set = {};    tally = Tally[partition];    For[j = 1, j <= Length[tally], j++,     set = Union[set, {tally[[j]][[2]]}]];    comp = Complement[Range[Max[set] + 1], set];    If[EvenQ[Min[comp]], count[n]++]    ]]; Table[count[i], {i, 1, nend}] CROSSREFS Cf. A000041, A300183. Sequence in context: A055529 A337723 A222735 * A338937 A319381 A340496 Adjacent sequences:  A299405 A299406 A299407 * A299409 A299410 A299411 KEYWORD nonn AUTHOR David S. Newman, Feb 20 2018 EXTENSIONS More terms from Alois P. Heinz, Feb 26 2018 STATUS approved

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Last modified September 22 22:38 EDT 2021. Contains 347609 sequences. (Running on oeis4.)