The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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