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 A079122 Number of ways to partition 2*n into distinct positive integers not greater than n. 7
 1, 0, 0, 1, 1, 3, 5, 8, 13, 21, 31, 46, 67, 95, 134, 186, 253, 343, 461, 611, 806, 1055, 1369, 1768, 2270, 2896, 3678, 4649, 5847, 7325, 9141, 11359, 14069, 17367, 21363, 26202, 32042, 39068, 47512, 57632, 69728, 84167, 101365, 121801, 146053, 174777 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Reinhard Zumkeller and Alois P. Heinz, Table of n, a(n) for n = 0..1000 (terms 0..80 from Reinhard Zumkeller) FORMULA a(n) = b(0, n), b(m, n) = 1 + sum(b(i, j): mn, 0, b(n-i, i-1))))     end: a:= n-> b(2*n, n): seq(a(n), n=0..80);  # Alois P. Heinz, Jan 18 2013 MATHEMATICA d[n_] := Select[IntegerPartitions[n], Max[Length /@ Split@ #] == 1 &]; Table[d[n], {n, 1, 12}] TableForm[%] f[n_] := Length[Select[d[2 n], First[#] <= n &]] Table[f[n], {n, 1, 20}]  (* A079122 *) (* Clark Kimberling, Mar 13 2012 *) b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, b[n, i-1] + If[i>n, 0, b[n-i, i-1]]]]; a[n_] := b[2*n, n]; Table[a[n], {n, 0, 80}] (* Jean-François Alcover, Oct 22 2015, after Alois P. Heinz *) PROG (Haskell) a079122 n = p [1..n] (2 * n) where    p _  0     = 1    p [] _     = 0    p (k:ks) m = if m < k then 0 else p ks (m - k) + p ks m -- Reinhard Zumkeller, Mar 16 2012 CROSSREFS Cf. A035294, A079126, A000009, A079124, A079125, A067953, A111133. Sequence in context: A227547 A163685 A080614 * A265069 A265070 A071679 Adjacent sequences:  A079119 A079120 A079121 * A079123 A079124 A079125 KEYWORD nonn AUTHOR Reinhard Zumkeller, Dec 27 2002 STATUS approved

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Last modified May 27 11:14 EDT 2017. Contains 287204 sequences.