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A026827
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Number of partitions of n into distinct parts, the least being 6.
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5
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0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 7, 8, 9, 11, 12, 14, 16, 18, 20, 23, 26, 29, 33, 37, 42, 47, 53, 59, 67, 74, 83, 93, 104, 115, 129, 143, 160, 177, 197, 218, 243, 268, 297, 329, 364, 401, 444, 489, 540, 595, 655, 721, 794, 872, 958
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OFFSET
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0,22
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LINKS
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FORMULA
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G.f.: x^6*Product_{j>=7} (1+x^j). - R. J. Mathar, Jul 31 2008
G.f.: Sum_{k>=1} x^(k*(k + 11)/2) / Product_{j=1..k-1} (1 - x^j). - Ilya Gutkovskiy, Nov 24 2020
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MAPLE
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b:= proc(n, i) option remember;
`if`(n=0, 1, `if`((i-6)*(i+7)/2<n, 0,
add(b(n-i*j, i-1), j=0..min(1, n/i))))
end:
a:= n-> `if`(n<6, 0, b(n-6$2)):
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MATHEMATICA
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b[n_, i_] := b[n, i] = If[n == 0, 1, If[(i-6)*(i+7)/2 < n, 0, Sum[b[n - i*j, i - 1], {j, 0, Min[1, n/i]}]]]; a[n_] := If[n < 6, 0, b[n-6, n-6]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Jun 24 2015, after Alois P. Heinz *)
Join[{0}, Table[Count[Last /@ Select[IntegerPartitions@n, DeleteDuplicates[#] == # &], 6], {n, 66}]] (* Robert Price, Jun 13 2020 *)
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CROSSREFS
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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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