OFFSET
0,8
COMMENTS
A composition of n is a finite sequence of positive integers summing to n.
For the operation of shortening all runs by 1, cuts-resistance is defined as the number of applications required to reach an empty word.
EXAMPLE
Triangle begins:
1
0 1
0 1 1
0 3 0 1
0 4 3 0 1
0 7 6 2 0 1
0 14 9 6 2 0 1
0 23 22 10 6 2 0 1
0 39 47 22 10 7 2 0 1
0 71 88 52 24 10 8 2 0 1
Row n = 6 counts the following compositions (empty columns not shown):
(6) (33) (222) (11112) (111111)
(15) (114) (1113) (21111)
(24) (411) (3111)
(42) (1122) (11121)
(51) (1131) (11211)
(123) (1221) (12111)
(132) (1311)
(141) (2112)
(213) (2211)
(231)
(312)
(321)
(1212)
(2121)
MATHEMATICA
degdep[q_]:=Length[NestWhileList[Join@@Rest/@Split[#]&, q, Length[#]>0&]]-1;
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], degdep[#]==k&]], {n, 0, 10}, {k, 0, n}]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Nov 23 2019
STATUS
approved