OFFSET
1,4
COMMENTS
Also the number of multisets of length n covering an initial interval of positive integers with more than one co-mode.
LINKS
John Tyler Rascoe, Table of n, a(n) for n = 1..1000
FORMULA
G.f.: Sum_{i>0} (x^(2*i) * (x-1)^3)/((x^i + x - 1)*(x^(i+1) + x - 1)^2). - John Tyler Rascoe, Jul 06 2024
EXAMPLE
The a(1) = 0 through a(6) = 21 compositions:
. (11) (111) (22) (113) (33)
(112) (131) (114)
(121) (311) (141)
(211) (1112) (222)
(1111) (1121) (411)
(1211) (1113)
(2111) (1122)
(11111) (1131)
(1212)
(1221)
(1311)
(2112)
(2121)
(2211)
(3111)
(11112)
(11121)
(11211)
(12111)
(21111)
(111111)
MATHEMATICA
Table[Length[Select[Join@@Permutations /@ IntegerPartitions[n], Count[#, Min@@#]>1&]], {n, 15}]
PROG
(PARI)
C_x(N)={my(x='x+O('x^N), h=sum(i=1, N, (x^(2*i)*(x-1)^3)/((x^i+x-1)*(x^(i+1)+x-1)^2))); concat([0], Vec(h))}
C_x(35) \\ John Tyler Rascoe, Jul 06 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 04 2023
STATUS
approved