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A374782
Number of partitions of n that do not have a fixed point that is also a fixed point of the conjugate partition.
1
1, 0, 2, 3, 4, 5, 8, 11, 17, 23, 33, 43, 60, 77, 104, 134, 177, 226, 295, 373, 480, 604, 766, 957, 1204, 1492, 1860, 2294, 2836, 3477, 4273, 5209, 6362, 7721, 9375, 11326, 13687, 16460, 19799, 23720, 28406, 33901, 40443, 48092, 57159, 67747, 80237, 94799
OFFSET
0,3
FORMULA
a(n) = A000041(n) - A188674(n) for n > 0, a(0) = 1.
EXAMPLE
a(0) = 1: the empty partition.
a(2) = 2: 2, 11.
a(3) = 3: 3, 21, 111.
a(4) = 4: 4, 31, 211, 1111.
a(5) = 5: 5, 41, 311, 2111, 11111.
a(6) = 8: 6, 33, 51, 222, 411, 3111, 21111, 111111.
a(7) = 11: 7, 43, 61, 322, 331, 511, 2221, 4111, 31111, 211111, 1111111.
MAPLE
b:= proc(n, i, p) option remember; `if`(n=0, 1,
`if`(i<1, 0, b(n, i-1, p)+add(`if`(i=p+j, 0,
b(n-i*j, min(n-i*j, i-1), p+j)), j=1..n/i)))
end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..47);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 19 2024
STATUS
approved