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A244164
Number of compositions of n in which the minimal multiplicity of parts equals 1.
11
1, 1, 3, 6, 15, 23, 53, 94, 203, 404, 855, 1648, 3416, 6662, 13400, 26406, 53038, 105306, 212051, 422162, 849267, 1696864, 3406077, 6807024, 13642099, 27268122, 54576003, 109096436, 218250874, 436243705, 872533347, 1744312748, 3488432736, 6974783481
OFFSET
1,3
LINKS
Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 1..2000 (first 400 terms from Alois P. Heinz)
Vaclav Kotesovec, Graph a(n)/2^n
FORMULA
a(n) = 2^(n-1) - A240085(n). - Gus Wiseman, Nov 25 2019
EXAMPLE
From Gus Wiseman, Nov 25 2019: (Start)
The a(1) = 1 through a(5) = 15 compositions:
(1) (2) (3) (4) (5)
(1,2) (1,3) (1,4)
(2,1) (3,1) (2,3)
(1,1,2) (3,2)
(1,2,1) (4,1)
(2,1,1) (1,1,3)
(1,2,2)
(1,3,1)
(2,1,2)
(2,2,1)
(3,1,1)
(1,1,1,2)
(1,1,2,1)
(1,2,1,1)
(2,1,1,1)
(End)
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, $max(1, k)..n/i])))
end:
a:= n-> b(n$2, 0, 1) -b(n$2, 0, 2):
seq(a(n), n=1..50);
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], Min@@Length/@Split[Sort[#]]==1&]], {n, 0, 10}] (* Gus Wiseman, Nov 25 2019 *)
CROSSREFS
Column k=1 of A242451.
The complement is counted by A240085.
Sequence in context: A087359 A253651 A180322 * A129602 A044888 A179805
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 21 2014
STATUS
approved