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A184644 Number of partitions of n having no parts with multiplicity 9. 8
1, 1, 2, 3, 5, 7, 11, 15, 22, 29, 42, 55, 76, 99, 133, 172, 227, 290, 376, 477, 612, 769, 975, 1217, 1528, 1895, 2359, 2907, 3592, 4400, 5403, 6584, 8034, 9742, 11823, 14272, 17234, 20713, 24897, 29803, 35674, 42542, 50719, 60272, 71592, 84794 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = A000041(n) - A183566(n).
a(n) = A183568(n,0) - A183568(n,9).
G.f.: Product_{j>0} (1-x^(9*j)+x^(10*j))/(1-x^j).
MAPLE
b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(i<1, [0, 0],
add((l->`if`(j=9, [l[1]$2], l))(b(n-i*j, i-1)), j=0..n/i)))
end:
a:= n-> (l-> l[1]-l[2])(b(n, n)):
seq(a(n), n=0..50);
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0, {1, 0}, If[i < 1, {0, 0}, Sum[Function[l, If[j == 9, {l[[1]], l[[1]]}, l]][b[n - i*j, i - 1]], {j, 0, n/i}]]];
a[n_] := b[n, n][[1]] - b[n, n][[2]];
Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Apr 30 2018, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A036008 A104502 A027343 * A209039 A182805 A309058
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jan 18 2011
STATUS
approved

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Last modified June 1 02:46 EDT 2023. Contains 363068 sequences. (Running on oeis4.)