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A110618
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Number of partitions of n with no part larger than n/2. Also partitions of n into n/2 or fewer parts.
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3
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1, 0, 1, 1, 3, 3, 7, 8, 15, 18, 30, 37, 58, 71, 105, 131, 186, 230, 318, 393, 530, 653, 863, 1060, 1380, 1686, 2164, 2637, 3345, 4057, 5096, 6158, 7665, 9228, 11395, 13671, 16765, 20040, 24418, 29098, 35251, 41869, 50460, 59755, 71669, 84626, 101050
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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FORMULA
| a(n) =A000041(n)-sum_{0<=i<n/2}A000041(i) = A000041(n)-A000070(floor[(n-1)/2]) = A110619(n, 2).
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EXAMPLE
| a(5) = 3 since 5 can be partitioned as 1+1+1+1+1, 2+1+1+1, or 2+2+1; not counted are 5, 4+1, or 3+2.
a(6) = 7 since 6 can be partitioned as 1+1+1+1+1+1, 1+1+1+1+2, 1+1+2+2, 2+2+2, 1+1+1+3, 1+2+3, 3+3; not counted are 1+1+4, 2+4, 1+5, 6.
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MAPLE
| A000070 := proc(n) add( combinat[numbpart](i), i=0..n) ; end proc:
A110618 := proc(n) combinat[numbpart](n) - A000070(floor((n-1)/2)) ; end proc: # R. J. Mathar, Jan 24 2011
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MATHEMATICA
| f[n_, 1] := 1; f[1, k_] := 1; f[n_, k_] := f[n, k] = If[k > n, f[n, k - 1], f[n, k - 1] + f[n - k, k]]; g[n_] := f[n, Floor[n/2]]; g[0] = 1; g[1] = 0; Array[g, 47, 0] (* Rorbert G. Wilson v, Jan 23 2011 *)
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CROSSREFS
| Sequence in context: A161416 A117989 A086543 * A108046 A116157 A056357
Adjacent sequences: A110615 A110616 A110617 * A110619 A110620 A110621
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KEYWORD
| nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Aug 01 2005
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