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A025151
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Number of partitions of n into distinct parts >= 6.
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4
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1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 7, 7, 9, 10, 12, 13, 16, 17, 20, 23, 26, 29, 34, 38, 43, 49, 55, 62, 70, 79, 88, 100, 111, 125, 140, 157, 174, 196, 217, 243, 270, 301, 333, 372, 411, 457, 506, 561, 619, 687, 757, 837, 924, 1019, 1122, 1238, 1361, 1498
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OFFSET
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0,14
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LINKS
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FORMULA
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G.f.: Sum_{k>=0} x^(k*(k + 11)/2) / Product_{j=1..k} (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-5)*(i+6)/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[#] >= 6 &]; Table[d[n], {n, 16}] (* strict partitions, parts >= 6 *)
Table[Length[d[n]], {n, 40}] (* A025151 for n >= 1 *)
b[n_, i_] := b[n, i] = If[n == 0, 1, If[(i - 5)(i + 6)/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, Aug 29 2016, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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