Stephen DeSalvo has authored 2 sequences.
A270638
Number of novel integer partitions with n parts.
Original entry on oeis.org
1, 0, 1, 1, 4, 14
Offset: 2
A182988
The number of dominance pairs of integer partitions of n according to either/or dominance order, where dominance between two partitions x and y means that x is majorized by y or y is majorized by x.
Original entry on oeis.org
1, 1, 4, 9, 25, 49, 117, 217, 454, 830, 1594, 2796, 5159, 8777, 15415, 25810, 43819, 71595, 118629, 190148, 307519, 485660, 769382, 1195807, 1864617, 2857630, 4384962, 6641332, 10052272, 15043925, 22501510, 33315580, 49267369, 72250341, 105746966, 153646123
Offset: 0
For n=1,2,3,4,5, a(n) = p(n)^2, since these values of n give a linear order for integer partitions.
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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, min(n-i,i), min(m-j,j), true))))
end:
a:= n-> 2*b(n$4, true)-combinat[numbpart](n):
seq(a(n), n=0..35); # Alois P. Heinz, Dec 09 2015
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b[n_, m_, i_, j_, t_] := b[n, m, i, j, t] = If[n0, b[n, m, i, j-1, True], 0] + b[n, m, i-1, j, False] + b[n-i, m-j, Min[n-i, i], Min[m-j, j], True]]]]; a[n_] := 2*b[n, n, n, n, True] - PartitionsP[n]; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Dec 09 2016 after Alois P. Heinz *)
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