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A025153
Number of partitions of n into distinct parts >= 8.
4
1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 8, 8, 10, 11, 13, 14, 17, 18, 21, 23, 26, 29, 33, 36, 41, 46, 51, 57, 64, 71, 79, 88, 97, 109, 120, 133, 147, 164, 180, 200, 220, 244, 268, 297, 325, 360, 395, 435, 477, 526, 575, 633, 693, 761, 832, 913
OFFSET
0,18
LINKS
FORMULA
a(n) = A026828(n+7). - R. J. Mathar, Jul 31 2008
G.f.: Product_{j>=8} (1+x^j). - R. J. Mathar, Jul 31 2008
G.f.: Sum_{k>=0} x^(k*(k + 15)/2) / Product_{j=1..k} (1 - x^j). - Ilya Gutkovskiy, Nov 24 2020
MAPLE
b:= proc(n, i) option remember;
`if`(n=0, 1, `if`((i-7)*(i+8)/2<n, 0,
add(b(n-i*j, i-1), j=0..min(1, n/i))))
end:
a:= n-> b(n$2):
seq(a(n), n=0..100); # Alois P. Heinz, Feb 07 2014
MATHEMATICA
d[n_] := Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 && Min[#] >= 8 &]; Table[d[n], {n, 20}] (* strict partitions, parts >= 8 *)
Table[Length[d[n]], {n, 40}] (* A025153 for n >= 1 *)
(* Clark Kimberling, Mar 07 2014 *)
CROSSREFS
Cf. A025147.
Sequence in context: A096401 A264593 A026828 * A026803 A286041 A027192
KEYWORD
nonn
STATUS
approved