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 A230025 Triangular array:  t(n, k) = number of occurrences of k as the number of outliers in all the partitions of n. 0
 1, 0, 2, 1, 0, 2, 1, 2, 0, 2, 1, 2, 2, 0, 2, 1, 2, 4, 2, 0, 2, 1, 4, 2, 4, 2, 0, 2, 2, 2, 6, 2, 6, 2, 0, 2, 2, 6, 2, 8, 2, 6, 2, 0, 2, 2, 4, 12, 2, 8, 2, 8, 2, 0, 2, 2, 8, 6, 14, 2, 10, 2, 8, 2, 0, 2, 3, 6, 14, 8, 18, 2, 10, 2, 10, 2, 0, 2, 3, 10, 10, 20, 10 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Definitions: the self-conjugate portion of a partition p is the portion of the Ferrers graph of p that remains unchanged when p is reflected about its principal diagonal.  The outliers of p are the nodes of the Ferrers graph that lie outside the self-conjugate portion of p. Sum of numbers in row n is A000041(n). LINKS EXAMPLE The first 9 rows: 1 0 2 1 0 2 1 2 0 2 1 2 2 0 2 1 2 4 2 0 2 1 4 2 4 2 0 2 2 2 6 2 6 2 0 2 2 6 2 8 2 6 2 0 2 The Ferrers graph of the partition p = [4,4,1,1] of 10 follows: 1 1 1 1 1 1 1 1 1 1 The self-conjugate portion of p is 1 1 1 1 1 1 1 1 so that the number of outliers of p is 2. MATHEMATICA ferrersMatrix[list_] := PadRight[Map[Table[1, {#}] &, #], {#, #} &[Max[#, Length[#]]]] &[list]; conjugatePartition[part_] := Table[Count[#, _?(# >= i &)], {i, First[#]}] &[part]; selfConjugatePortion[list_] := ferrersMatrix[#]*ferrersMatrix[conjugatePartition[#]] &[list]; outliers[list_] := Count[Flatten[ferrersMatrix[#] - selfConjugatePortion[#] &[list]], 1]; a[n_] := Map[outliers, IntegerPartitions[n]]; t = Table[Count[a[n], k], {n, 1, 13}, {k, 0, n - 1}] u = Flatten[t] (* Peter J. C. Moses, Feb 21 2014 *) CROSSREFS Cf. A000041. Sequence in context: A217522 A287520 A130094 * A207869 A130210 A236459 Adjacent sequences:  A230022 A230023 A230024 * A230026 A230027 A230028 KEYWORD nonn,tabl,easy AUTHOR Clark Kimberling, Feb 23 2014 STATUS approved

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Last modified November 17 22:28 EST 2018. Contains 317279 sequences. (Running on oeis4.)