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 A265508 Number of unordered pairs {p,q} of partitions of n into distinct parts such that p and q are incomparable in the dominance order. 3
 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 5, 10, 15, 29, 42, 68, 109, 162, 240, 364, 527, 749, 1096, 1529, 2162, 3026, 4179, 5702, 7926, 10650, 14412, 19437, 26042, 34560, 46077, 60617, 79893, 104850, 136851, 177884, 231526, 298868, 385221, 496159, 635725, 812342 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,12 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..250 Wikipedia, Dominance Order FORMULA a(n) = A000217(A000009(n)) - A265506(n). EXAMPLE a(9) = 1: {621,54}. a(10) = 1: {721,64}. a(11) = 3: {821,74}, {821,65}, {731,65}. a(12) = 5: {6321,543}, {921,84}, {921,75}, {831,75}, {732,651}. MAPLE b:= proc(n, m, i, j, t) option remember; `if`(n0, b(n, m, i, j-1, true), 0)+ b(n, m, i-1, j, false)+b(n-i, m-j, max(0, min(n-i, i-1)), max(0, min(m-j, j-1)), true)))) end: g:= proc(n, i) option remember; `if`(i*(i+1)/2n, 0, g(n-i, i-1)))) end: a:= n-> (t-> t*(t+1)/2)(g(n\$2))-b(n\$4, true): seq(a(n), n=0..45); MATHEMATICA b[n_, m_, i_, j_, t_] := b[n, m, i, j, t] = If[n < m, 0, If[n == 0, 1, If[i < 1, 0, If[t && j > 0, b[n, m, i, j-1, True], 0] + b[n, m, i-1, j, False] + b[n-i, m-j, Max[0, Min[n-i, i-1]], Max[0, Min[m-j, j-1]], True]]]]; g[n_, i_] := g[n, i] = If[i*(i+1)/2 < n, 0, If[n == 0, 1, g[n, i-1] + If[i > n, 0, g[n-i, i-1]]]]; a[n_] := (#*(#+1)/2&)[g[n, n]] - b[n, n, n, n, True]; Table[a[n], {n, 0, 45}] (* Jean-François Alcover, Feb 05 2017, translated from Maple *) CROSSREFS Cf. A000009, A000217, A248476, A265506. Sequence in context: A077285 A072523 A054473 * A327042 A006168 A250115 Adjacent sequences: A265505 A265506 A265507 * A265509 A265510 A265511 KEYWORD nonn AUTHOR Alois P. Heinz, Dec 09 2015 STATUS approved

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Last modified September 18 02:51 EDT 2024. Contains 375995 sequences. (Running on oeis4.)