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A026829
Number of partitions of n into distinct parts, the least being 8.
4
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 8, 9, 10, 12, 13, 15, 17, 19, 21, 24, 26, 29, 33, 36, 40, 45, 50, 55, 62, 68, 76, 84, 93, 102, 114, 125, 138, 152, 168, 184, 204, 223, 246, 270, 297, 325, 358, 391, 429, 470
OFFSET
0,28
LINKS
FORMULA
a(n) = A025154(n-8), n>8. - R. J. Mathar, Jul 31 2008
G.f.: x^8*Product_{j>=9} (1+x^j). - R. J. Mathar, Jul 31 2008
G.f.: Sum_{k>=1} x^(k*(k + 15)/2) / Product_{j=1..k-1} (1 - x^j). - Ilya Gutkovskiy, Nov 24 2020
MAPLE
b:= proc(n, i) option remember;
`if`(n=0, 1, `if`((i-8)*(i+9)/2<n, 0,
add(b(n-i*j, i-1), j=0..min(1, n/i))))
end:
a:= n-> `if`(n<8, 0, b(n-8$2)):
seq(a(n), n=0..100); # Alois P. Heinz, Feb 07 2014
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0, 1, If[(i-8)*(i+9)/2 < n, 0, Sum[b[n - i*j, i - 1], {j, 0, Min[1, n/i]}]]]; a[n_] := If[n < 8, 0, b[n-8, n-8]]; 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[#] == # &], 8], {n, 66}]] (* Robert Price, Jun 13 2020 *)
CROSSREFS
Sequence in context: A025159 A373073 A264594 * A025154 A241827 A373067
KEYWORD
nonn
STATUS
approved