login
A212544
Number of partitions of n containing at least one part m-4 if m is the largest part.
2
0, 0, 1, 1, 3, 4, 8, 11, 18, 24, 37, 48, 69, 89, 122, 155, 207, 259, 337, 419, 534, 657, 827, 1008, 1252, 1518, 1864, 2246, 2736, 3276, 3960, 4722, 5668, 6727, 8032, 9492, 11274, 13279, 15696, 18424, 21694, 25380, 29772, 34736, 40604, 47244, 55060, 63897
OFFSET
4,5
LINKS
FORMULA
G.f.: Sum_{i>0} x^(2*i+4) / Product_{j=1..4+i} (1-x^j).
EXAMPLE
a(6) = 1: [5,1].
a(7) = 1: [5,1,1].
a(8) = 3: [5,1,1,1], [5,2,1], [6,2].
a(9) = 4: [5,1,1,1,1], [5,2,1,1], [5,3,1], [6,2,1].
a(10) = 8: [5,1,1,1,1,1], [5,2,1,1,1], [5,2,2,1], [5,3,1,1], [5,4,1], [6,2,1,1], [6,2,2], [7,3].
MAPLE
b:= proc(n, i) option remember;
`if`(n=0 or i=1, 1, b(n, i-1)+`if`(i>n, 0, b(n-i, i)))
end:
a:= n-> add(b(n-2*m-4, min(n-2*m-4, m+4)), m=1..(n-4)/2):
seq(a(n), n=4..60);
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0 || i == 1, 1, b[n, i - 1] + If[i > n, 0, b[n - i, i]]];
a[n_] := Sum[b[n - 2 m - 4, Min[n - 2 m - 4, m + 4]], {m, 1, (n - 4)/2}];
a /@ Range[4, 60] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)
CROSSREFS
Column k=4 of A212551.
Sequence in context: A099108 A208971 A001994 * A349801 A320787 A183151
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 20 2012
STATUS
approved