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A227552
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Number of partitions of n into distinct parts with maximal boundary size.
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3
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1, 1, 1, 1, 1, 2, 3, 1, 2, 2, 4, 6, 1, 1, 3, 4, 6, 9, 14, 1, 2, 3, 5, 8, 11, 17, 24, 1, 1, 3, 5, 8, 11, 18, 24, 35, 49, 1, 2, 3, 6, 9, 14, 21, 30, 42, 60, 81, 1, 1, 3, 5, 9, 13, 21, 29, 43, 60, 84, 113, 156, 1, 2, 3, 6, 10, 15, 24, 35, 50, 71, 99, 134, 184, 246
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OFFSET
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0,6
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COMMENTS
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The boundary size is the number of parts having less than two neighbors.
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LINKS
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FORMULA
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MAPLE
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b:= proc(n, i, t) option remember; `if`(n=0, `if`(t>1, x, 1),
expand(`if`(i<1, 0, `if`(t>1, x, 1)*b(n, i-1, iquo(t, 2))+
`if`(i>n, 0, `if`(t=2, x, 1)*b(n-i, i-1, iquo(t, 2)+2)))))
end:
a:= n-> (p->coeff(p, x, degree(p)))(b(n$2, 0)):
seq(a(n), n=0..100);
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MATHEMATICA
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b[n_, i_, t_] := b[n, i, t] = If[n==0, If[t>1, x, 1], Expand[If[i<1, 0, If[t>1, x, 1]*b[n, i-1, Quotient[t, 2]] + If[i>n, 0, If[t==2, x, 1] * b[n-i, i-1, Quotient[t, 2]+2]]]]]; a[n_] := Function [p, Coefficient[p, x, Exponent[p, x]]][b[n, n, 0]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Feb 15 2017, translated from Maple *)
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CROSSREFS
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Last nonzero elements of rows of A227345.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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