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A222704 Total number of parts of multiplicity 4 in all partitions of n. 2
1, 0, 1, 1, 3, 3, 5, 6, 11, 13, 20, 24, 37, 45, 64, 80, 110, 137, 184, 229, 303, 375, 486, 602, 772, 951, 1202, 1478, 1853, 2267, 2817, 3432, 4236, 5142, 6300, 7620, 9284, 11185, 13553, 16273, 19625, 23478, 28187, 33613, 40192, 47778, 56904, 67443, 80051 (list; graph; refs; listen; history; text; internal format)
OFFSET
4,5
LINKS
FORMULA
G.f.: (x^4/(1-x^4)-x^5/(1-x^5))/Product_{j>0}(1-x^j).
a(n) ~ exp(Pi*sqrt(2*n/3)) / (40*Pi*sqrt(2*n)). - Vaclav Kotesovec, May 24 2018
MAPLE
b:= proc(n, p) option remember; `if`(n=0, [1, 0], `if`(p<1, [0, 0],
add((l->`if`(m=4, l+[0, l[1]], l))(b(n-p*m, p-1)), m=0..n/p)))
end:
a:= n-> b(n, n)[2]:
seq(a(n), n=4..60);
MATHEMATICA
b[n_, p_] := b[n, p] = If[n == 0, {1, 0}, If[p<1, {0, 0}, Sum[Function[l, If[m == 4, l + {0, l[[1]]}, l]][b[n - p*m, p - 1]], {m, 0, n/p}]]];
a[n_] := b[n, n][[2]];
Table[a[n], {n, 4, 60}] (* Jean-François Alcover, Apr 30 2018, after Alois P. Heinz *)
CROSSREFS
Column k=4 of A197126.
Sequence in context: A276434 A183561 A300183 * A095950 A089874 A092035
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 28 2013
STATUS
approved

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Last modified May 27 14:41 EDT 2024. Contains 372861 sequences. (Running on oeis4.)