OFFSET
0,4
COMMENTS
The weakly decreasing run-leaders of a sequence are obtained by splitting it into maximal weakly decreasing subsequences and taking the first term of each.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (1,1,0,-1,-1,1).
FORMULA
G.f.: x^3*(2 + x + x^2)/((1 + x + x^2)*(1 + x)*(1 - x)^3). - Andrew Howroyd, Aug 14 2024
EXAMPLE
The a(0) = 0 through a(8) = 17 compositions:
. . . (3) (31) (32) (33) (322) (332)
(12) (112) (122) (321) (331) (3221)
(121) (311) (1122) (1222) (3311)
(1112) (1221) (3211) (11222)
(1121) (3111) (11122) (12221)
(1211) (11112) (11221) (32111)
(11121) (12211) (111122)
(11211) (31111) (111221)
(12111) (111112) (112211)
(111121) (122111)
(111211) (311111)
(112111) (1111112)
(121111) (1111121)
(1111211)
(1112111)
(1121111)
(1211111)
MATHEMATICA
Table[Length[Select[Join@@Permutations /@ IntegerPartitions[n], Total[First/@Split[#, GreaterEqual]]==3&]], {n, 0, 15}]
PROG
(PARI) seq(n)={Vec((2 + x + x^2)/((1 + x + x^2)*(1 + x)*(1 - x)^3) + O(x^(n-2)), -n-1)} \\ Andrew Howroyd, Aug 14 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gus Wiseman, Aug 12 2024
EXTENSIONS
a(27) onwards from Andrew Howroyd, Aug 14 2024
STATUS
approved