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A243119
Number of compositions of n in which the maximal multiplicity of parts equals 2.
2
1, 0, 4, 6, 10, 21, 40, 87, 121, 219, 421, 690, 1159, 1782, 3304, 5190, 8212, 12897, 22084, 33255, 53617, 82539, 124849, 206172, 313339, 472056, 714976, 1077996, 1682806, 2502645, 3804460, 5674305, 8340535, 12245241, 18851899, 27570366, 40385431, 59314572
OFFSET
2,3
LINKS
FORMULA
a(n) = A232432(n) - A032020(n) = A243081(n,2) - A243081(n,1).
EXAMPLE
a(6) = 10: [1,1,2,2], [1,2,1,2], [1,2,2,1], [2,1,1,2], [2,1,2,1], [2,2,1,1], [3,3], [1,1,4], [1,4,1], [4,1,1].
MAPLE
b:= proc(n, i, p, k) option remember; `if`(n=0, p!, `if`(i<1, 0,
add(b(n-i*j, i-1, p+j, k)/j!, j=0..min(n/i, k))))
end:
a:= n-> b(n$2, 0, 2) -b(n$2, 0, 1):
seq(a(n), n=2..45);
CROSSREFS
Column k=2 of A242447.
Sequence in context: A277455 A320124 A185913 * A277343 A077065 A131867
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 29 2014
STATUS
approved