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 A237194 Triangular array:  T(n,k) = number of strict partitions P of n into positive parts such that P includes a partition of k. 2
 1, 0, 1, 1, 1, 2, 1, 0, 1, 2, 1, 1, 1, 1, 3, 2, 2, 1, 2, 2, 4, 2, 2, 2, 2, 2, 2, 5, 3, 2, 3, 1, 3, 2, 3, 6, 3, 3, 4, 3, 3, 4, 3, 3, 8, 5, 4, 5, 4, 3, 4, 5, 4, 5, 10, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 12, 7, 6, 7, 7, 7, 4, 7, 7, 7, 6, 7, 15, 8, 7, 8, 8, 8, 8, 8 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS (Col 1) = A025147; (Col 2) = A015744; T(n,n) = A000009(n); T(2n,n) = A237258; T(n,k) = T(n,n-k) for k=1..n-1, n >= 2. LINKS Clark Kimberling, Table of n, a(n) for n = 1..1000 EXAMPLE First 13 rows: 1 0 1 1 1 2 1 0 1 2 1 1 1 1 3 2 2 1 2 2 4 2 2 2 2 2 2 5 3 2 3 1 3 2 3 6 3 3 4 3 3 4 3 3 8 5 4 5 4 3 4 5 4 5 10 5 5 5 5 5 5 5 5 5 5 12 7 6 7 7 7 4 7 7 7 6 7 15 8 7 8 8 8 8 8 8 8 8 7 8 18 T(12,4) = 7 counts these partitions:  [8,4], [8,3,1], [7,4,1], [6,4,2], [6,3,2,1], [5,4,3], [5,4,2,1]. MATHEMATICA Table[theTotals = Map[{#, Map[Total, Subsets[#]]} &, Select[IntegerPartitions[nn], # == DeleteDuplicates[#] &]]; Table[Length[Map[#[[1]] &, Select[theTotals, Length[Position[#[[2]], sumTo]] >= 1 &]]], {sumTo, nn}], {nn, 45}] // TableForm u = Flatten[%]  (* Peter J. C. Moses, Feb 04 2014 *) CROSSREFS Cf. A000009, A237258. Sequence in context: A178948 A203827 A194289 * A143519 A307778 A029376 Adjacent sequences:  A237191 A237192 A237193 * A237195 A237196 A237197 KEYWORD nonn,tabl,easy AUTHOR Clark Kimberling, Feb 05 2014 STATUS approved

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Last modified January 27 17:58 EST 2020. Contains 331296 sequences. (Running on oeis4.)