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 A337586 Triangle read by rows: T(n, k) is the number of integer multisets of size k (partitions of k) for which the number of partitions of n with matching multiplicity multiset is odd (n >= 1, 1 <= k <= n). 1
 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 0, 0, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 3, 3, 2, 1, 1, 1, 0, 3, 0, 3, 3, 2, 1, 1, 1, 1, 0, 3, 3, 3, 3, 2, 1, 1, 1, 1, 2, 3, 2, 1, 5, 3, 2, 1, 1, 1, 2, 2, 1, 3, 7, 3, 5, 3, 2, 1, 1, 1, 0, 0, 2, 2, 2, 5, 3, 5, 3, 2, 1, 1, 1, 1, 0, 3, 3, 4, 5, 5, 3, 5, 3 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS The relevant partitions of n have exactly k parts. The number of multiplicity multisets of size k met by a positive even number of partitions of n is A337584(n, k) - T(n, k). LINKS Álvar Ibeas, First 72 rows, flattened Álvar Ibeas, First 30 rows FORMULA T(n, k) == A008284(n, k) (mod 2). If k > (2*n+1)/3, T(n, k) = A337585(n - k). EXAMPLE The 3 = A008284(6, 2) partitions of 6 into 2 parts show 2 = A337584(6, 2) different multiplicity multisets: (1, 1) is attained by two of those partitions ((5, 1) and (4, 2)) and the other (2) just by one, (3, 3). Then, T(6, 2) = 1. Triangle begins:   k:  1 2 3 4 5 6 7 8 9 10       -------------------- n=1:  1 n=2:  1 1 n=3:  1 1 1 n=4:  1 2 1 1 n=5:  1 0 0 1 1 n=6:  1 1 3 2 1 1 n=7:  1 1 2 1 2 1 1 n=8:  1 2 1 3 3 2 1 1 n=9:  1 0 3 0 3 3 2 1 1 n=10: 1 1 0 3 3 3 3 2 1 1 CROSSREFS Cf. A008284, A337585 (row sums), A337584. Sequence in context: A005091 A276516 A253638 * A345006 A086831 A191340 Adjacent sequences:  A337583 A337584 A337585 * A337587 A337588 A337589 KEYWORD nonn,tabl AUTHOR Álvar Ibeas, Sep 02 2020 STATUS approved

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Last modified June 15 12:29 EDT 2021. Contains 345048 sequences. (Running on oeis4.)