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A025149
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Number of partitions of n into distinct parts >= 4.
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6
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1, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 6, 6, 8, 9, 11, 12, 15, 17, 20, 23, 27, 31, 36, 41, 47, 55, 62, 71, 81, 93, 105, 120, 135, 154, 174, 197, 221, 251, 281, 317, 356, 400, 447, 502, 561, 628, 701, 782, 871, 972, 1081, 1202, 1336, 1483, 1645, 1825, 2021, 2237, 2476, 2736
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OFFSET
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0,10
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LINKS
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FORMULA
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G.f.: sum(n>=0, x^(n*(n+7)/2) / prod(k=1..n, 1-x^k) ); special case of g.f. for partitions into distinct parts >= L, sum(n>=0, x^(n*(n+2*L-1)/2) / prod(k=1..n, 1-x^k) ). - Joerg Arndt, Mar 24 2011
a(n) + a(n+1) + a(n+2) + 2*a(n+3) + a(n+4) + a(n+5) + a(n+6) = A000009(n+6).
(End)
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MAPLE
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g:=product(1+x^(j), j=4..54): gser:=series(g, x=0, 55): seq(coeff(gser, x, n), n=0..53); # Zerinvary Lajos, Mar 09 2007
# second Maple program:
b:= proc(n, i) option remember;
`if`(n=0, 1, `if`((i-3)*(i+4)/2<n, 0,
add(b(n-i*j, i-1), j=0..min(1, n/i))))
end:
a:= n-> b(n$2):
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MATHEMATICA
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d[n_] := Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 && Min[#] >= 4 &]; Table[d[n], {n, 12}] (* strict partitions, parts >= 4 *)
Table[Length[d[n]], {n, 40}] (* A025149 for n >= 1 *)
b[n_, i_] := b[n, i] = If[n==0, 1, If[(i-3)*(i+4)/2<n, 0, Sum[b[n-i*j, i-1], {j, 0, Min[1, n/i]}]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Oct 22 2015, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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