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A244164 Number of compositions of n in which the minimal multiplicity of parts equals 1. 9
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 (list; graph; refs; listen; history; text; internal format)
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.

Cf. A003242, A098504, A114901, A261983, A329740, A329741.

Sequence in context: A087359 A253651 A180322 * A129602 A044888 A179805

Adjacent sequences:  A244161 A244162 A244163 * A244165 A244166 A244167

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 21 2014

STATUS

approved

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Last modified May 14 22:40 EDT 2021. Contains 343909 sequences. (Running on oeis4.)