OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = Sum_{k=floor(n/3)..floor(n/2)} C(2*n-4*k,n-2*k)*C(n-1-k,2*n-4*k-1).
Recurrence: n*(2*n-7)*a(n) = 2*(n-2)*(2*n-5)*a(n-2) + 2*(2*n-7)*(2*n-3)*a(n-3) - (n-4)*(2*n-3)*a(n-4). - Vaclav Kotesovec, May 01 2014
a(n) ~ sqrt(c) * d^n / sqrt(Pi*n), where d = 1.94696532812840456026081823863... is the root of the equation 1-4*d-2*d^2+d^4 = 0, c = 0.225563290820392765554898545739... is the root of the equation 43*c^4-18*c^2+8*c-1=0. - Vaclav Kotesovec, May 01 2014
EXAMPLE
From Gus Wiseman, Jun 26 2022: (Start)
The a(0) = 1 through a(7) = 6 compositions (empty columns indicated by dots):
() . . (12) . (14) (1122) (16)
(21) (23) (1212) (25)
(32) (1221) (34)
(41) (2112) (43)
(2121) (52)
(2211) (61)
(End)
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], Count[#, _?EvenQ]==Count[#, _?OddQ]&]], {n, 0, 15}] (* Gus Wiseman, Jun 26 2022 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Sep 24 2004
STATUS
approved