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A096749
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Number of partitions of n into distinct parts, the least being 2.
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7
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0, 0, 1, 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 9, 10, 12, 15, 17, 20, 24, 28, 32, 38, 44, 51, 59, 68, 78, 91, 103, 118, 136, 155, 176, 201, 228, 259, 294, 332, 375, 425, 478, 538, 607, 681, 764, 858, 961, 1075, 1203, 1343, 1499, 1673, 1863, 2073, 2308, 2564, 2847, 3161, 3504
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OFFSET
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0,10
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COMMENTS
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The old entry with this sequence number was a duplicate of A071569.
a(n), n>2 is the Euler transform of [0,0,1,1,1] joined with period [0,1]. - Georg Fischer, Aug 15 2020
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LINKS
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FORMULA
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G.f.: x^2*Product_{j>=3} (1+x^j). - R. J. Mathar, Jul 31 2008
G.f.: Sum_{k>=1} x^(k*(k + 3)/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-2)*(i+3)/2<n, 0,
add(b(n-i*j, i-1), j=0..min(1, n/i))))
end:
a:= n-> `if`(n<2, 0, b(n-2$2)):
# Using the function EULER from Transforms (see link at the bottom of the page).
[0, 0, 1, op(EULER([0, 0, 1, 1, seq(irem(n, 2), n=1..57)]))]; # Peter Luschny, Aug 19 2020
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MATHEMATICA
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b[n_, i_] := b[n, i] = If[n == 0, 1, If[(i-2)*(i+3)/2<n, 0, Sum[b[n-i*j, i-1], {j, 0, Min[1, n/i]}]]]; a[n_] := If[n<2, 0, b[n-2, n-2]]; Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Oct 13 2014, after Alois P. Heinz *)
Join[{0}, Table[Count[Last /@ Select[IntegerPartitions@n, DeleteDuplicates[#] == # &], 2], {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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