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 A079126 Triangle T(n,k) of numbers of partitions of n into distinct positive integers <= k, 0<=k<=n. 6
 1, 0, 1, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 1, 2, 0, 0, 0, 1, 2, 3, 0, 0, 0, 1, 2, 3, 4, 0, 0, 0, 0, 2, 3, 4, 5, 0, 0, 0, 0, 1, 3, 4, 5, 6, 0, 0, 0, 0, 1, 3, 5, 6, 7, 8, 0, 0, 0, 0, 1, 3, 5, 7, 8, 9, 10, 0, 0, 0, 0, 0, 2, 5, 7, 9, 10, 11, 12, 0, 0, 0, 0, 0, 2, 5, 8, 10, 12, 13, 14, 15, 0, 0, 0, 0, 0, 1, 4, 8, 11, 13, 15, 16, 17, 18 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,10 COMMENTS T(n,n) = A000009(n), right side of the triangle; T(n,k)=0 for n>0 and k < A002024(n); T(prime(n),n) = A067953(n) for n>0. LINKS Alois P. Heinz, Rows n = 0..140, flattened Eric Weisstein's World of Mathematics, Partition Function Q. FORMULA T(n,k) = b(0,n,k), where b(m,n,k) = 1+sum(b(i,j,k): mn, 0, T(n-i, i-1)))) end: seq(seq(T(n, k), k=0..n), n=0..20); # Alois P. Heinz, May 11 2015 MATHEMATICA T[n_, i_] := T[n, i] = If[n==0, 1, If[i<1, 0, T[n, i-1] + If[i>n, 0, T[n-i, i-1]]]]; Table[Table[T[n, k], {k, 0, n}], {n, 0, 20}] // Flatten (* Jean-François Alcover, Jun 30 2015, after Alois P. Heinz *) CROSSREFS Cf. A000009, A079122, A035294, A079124, A079125. Differs from A026840 in having extra zeros at the ends of the rows. Sequence in context: A132406 A197881 A332712 * A339086 A186336 A025891 Adjacent sequences: A079123 A079124 A079125 * A079127 A079128 A079129 KEYWORD nonn,tabl AUTHOR Reinhard Zumkeller, Dec 27 2002 STATUS approved

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Last modified September 18 20:16 EDT 2024. Contains 376002 sequences. (Running on oeis4.)