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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.)