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 A369696 Number of unordered pairs (p,q) of partitions of n such that the set of parts in q is equal to the set of parts in p. 3
 1, 1, 2, 3, 5, 8, 12, 19, 27, 42, 61, 91, 130, 192, 271, 401, 556, 802, 1126, 1597, 2217, 3132, 4315, 6003, 8257, 11370, 15527, 21251, 28798, 39043, 52722, 70911, 95047, 127155, 169431, 225072, 298362, 393946, 519294, 682090, 894251, 1168258, 1524370, 1981554 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..350 FORMULA a(n) = (A000041(n) + A369695(n))/2. EXAMPLE a(5) = 8: (11111, 11111), (2111, 2111), (2111, 221), (221, 221), (311, 311), (32, 32), (41, 41), (5, 5). MAPLE b:= proc(n, m, i) option remember; `if`(n=0, `if`(m=0, 1, 0), `if`(i<1, 0, b(n, m, i-1)+add(add( b(sort([n-i*j, m-i*h])[], i-1), h=1..m/i), j=1..n/i))) end: a:= n-> (b(n\$3)+combinat[numbpart](n))/2: seq(a(n), n=0..50); MATHEMATICA b[n_, m_, i_] := b[n, m, i] = If[n == 0, If[m == 0, 1, 0], If[i < 1, 0, b[n, m, i-1] + Sum[Sum[b[Sequence @@ Sort[{n-i*j, m-i*h}], i-1], {h, 1, m/i}], {j, 1, n/i}]]]; a[n_] := (b[n, n, n] + PartitionsP[n])/2; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Feb 29 2024, after Alois P. Heinz *) CROSSREFS Cf. A000041, A297388, A369695, A369697. Sequence in context: A086676 A055804 A267372 * A355975 A327421 A124062 Adjacent sequences: A369693 A369694 A369695 * A369697 A369698 A369699 KEYWORD nonn AUTHOR Alois P. Heinz, Jan 29 2024 STATUS approved

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Last modified August 12 09:11 EDT 2024. Contains 375085 sequences. (Running on oeis4.)