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A232432 Number of compositions of n avoiding the pattern 111. 7
1, 1, 2, 3, 7, 11, 21, 34, 59, 114, 178, 284, 522, 823, 1352, 2133, 3739, 5807, 9063, 14074, 23639, 36006, 56914, 87296, 131142, 214933, 324644, 487659, 739291, 1108457, 1724673, 2558386, 3879335, 5772348, 8471344, 12413666, 19109304, 27886339, 40816496 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of compositions of n into parts with multiplicity <= 2.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

EXAMPLE

a(4) = 7: [4], [3,1], [2,2], [1,3], [2,1,1], [1,2,1], [1,1,2].

a(5) = 11: [5], [4,1], [3,2], [2,3], [1,4], [3,1,1], [2,2,1], [1,3,1], [2,1,2], [1,2,2], [1,1,3].

a(6) = 21: [6], [4,2], [3,3], [5,1], [2,4], [1,5], [2,1,3], [1,2,3], [1,1,4], [4,1,1], [3,2,1], [2,3,1], [1,4,1], [3,1,2], [1,3,2], [1,2,2,1], [2,1,1,2], [1,2,1,2], [1,1,2,2], [2,2,1,1], [2,1,2,1].

MAPLE

b:= proc(n, i, p) option remember; `if`(n=0, p!, `if`(i<1, 0,

      add(b(n-i*j, i-1, p+j)/j!, j=0..min(n/i, 2))))

    end:

a:= n-> b(n$2, 0):

seq(a(n), n=0..50);

MATHEMATICA

f[list_]:=Apply[And, Table[Count[list, i]<3, {i, 1, Max[list]}]]; g[list_]:=Length[list]!/Apply[Times, Table[Count[list, i]!, {i, 1, Max[list]}]]; Table[Total[Map[g[#]&, Select[Partitions[n], f[#]&]]], {n, 1, 35}] (* Geoffrey Critzer, Nov 25 2013 *)

CROSSREFS

Cf. A000726 (partitions avoiding 111), A032020 (pattern 11), A128695 (adjacent pattern 111).

Column k=2 of A243081.

Sequence in context: A014529 A095015 A024367 * A037078 A034431 A095766

Adjacent sequences:  A232429 A232430 A232431 * A232433 A232434 A232435

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 23 2013

STATUS

approved

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Last modified April 7 14:29 EDT 2020. Contains 333305 sequences. (Running on oeis4.)