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A232464 Number of compositions of n avoiding the pattern 1111. 5
1, 1, 2, 4, 7, 15, 26, 52, 93, 173, 310, 556, 1041, 1789, 3098, 5620, 9725, 16377, 28764, 48518, 82889, 137161, 237502, 390084, 646347, 1055975, 1774036, 2907822, 4698733, 7581093, 12381660, 19891026, 32113631, 51110319, 80777888, 130175410, 204813395 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of compositions of n into parts with multiplicity <= 3.

LINKS

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

EXAMPLE

a(5) = 15: [5], [4,1], [3,2], [2,3], [1,4], [1,2,2], [2,1,2], [1,1,3], [3,1,1], [2,2,1], [1,3,1], [1,2,1,1], [2,1,1,1], [1,1,2,1], [1,1,1,2].

a(6) = 26: [6], [3,3], [5,1], [4,2], [2,4], [1,5], [4,1,1], [3,2,1], [2,3,1], [1,4,1], [3,1,2], [2,2,2], [1,3,2], [1,2,3], [2,1,3], [1,1,4], [1,2,2,1], [2,1,2,1], [1,1,3,1], [3,1,1,1], [2,2,1,1], [1,3,1,1], [1,2,1,2], [2,1,1,2], [1,1,2,2], [1,1,1,3].

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, 3))))

    end:

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

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

MATHEMATICA

f[list_]:=Apply[And, Table[Count[list, i]<4, {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. A001935 (partitions avoiding 1111), A032020 (pattern 11), A232432 (pattern 111), A232394 (consecutive pattern 1111).

Column k=3 of A243081.

Sequence in context: A002956 A171276 A027167 * A264292 A259592 A291220

Adjacent sequences:  A232461 A232462 A232463 * A232465 A232466 A232467

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 24 2013

STATUS

approved

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Last modified October 17 21:14 EDT 2018. Contains 316293 sequences. (Running on oeis4.)