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 A209354 Triangular array:  T(n,k) = number of partitions of n for which (maximal term)-(minimal term)=k, if 0<=k
 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 1, 1, 0, 1, 1, 3, 1, 1, 0, 1, 3, 2, 3, 1, 1, 0, 1, 1, 5, 3, 3, 1, 1, 0, 1, 3, 4, 6, 3, 3, 1, 1, 0, 1, 2, 6, 6, 7, 3, 3, 1, 1, 0, 1, 3, 6, 10, 7, 7, 3, 3, 1, 1, 0, 1, 1, 9, 10, 12, 8, 7, 3, 3, 1, 1, 0, 1, 5, 6, 15, 14, 13, 8, 7, 3, 3, 1, 1, 0, 1, 1, 11, 15, 20 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,11 COMMENTS Row sums:  A000041 (number of partitions of n) LINKS EXAMPLE First ten rows: 1 0 1 1 0 1 1 1 0 1 2 1 1 0 1 1 3 1 1 0 1 3 2 3 1 1 0 1 1 5 3 3 1 1 0 1 3 4 6 3 3 1 1 0 1 2 6 6 7 3 3 1 1 0 1 Row 5 (counting the top row as row 0): T(5,0)=1 counts [1,1,1,1,1] T(5,1)=3 counts [2,1,1,1], [2,2,1], [3,2] T(5,2)=1 counts [3,1,1] T(5,3)=1 counts [4,1] T(5,4)=0 T(5,5)=1 counts [5] MATHEMATICA f[n_] := IntegerPartitions[n]; p[n_, k_] := f[n][[k]]; r[n_] := Table[p[n, k], {k, 1, Length[f[n]]}] g[n_, k_] := Max[p[n, k]] - Min[p[n, k]]; g[n_, 1] := n; t[n_] := Table[g[n, k], {k, 1, Length[f[n]]}] c[0, 0] = 1; c[n_, k_] := Count[t[n], k] u = Table[c[n, k], {n, 0, 15}, {k, 0, n}]; TableForm[u] (* as an triangle *) Flatten[u]   (* as a sequence *) CROSSREFS Cf. A000041. Sequence in context: A147809 A217605 A096651 * A294446 A318163 A114640 Adjacent sequences:  A209351 A209352 A209353 * A209355 A209356 A209357 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 06 2012 STATUS approved

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Last modified December 12 03:27 EST 2018. Contains 318052 sequences. (Running on oeis4.)