OFFSET
0,8
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
EXAMPLE
a(11) counts these 6 partitions: 821, 722, 641, 632, 542, 443.
MAPLE
b:= proc(n, i, t) option remember;
`if`(n=0, `if`(t=0, 1, 0), `if`(i<1, 0, b(n, i-1, t)+
`if`(i>n, 0, b(n-i, i, t+`if`(irem(i, 2)=1, 2, -1)))))
end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..60); # Alois P. Heinz, Mar 14 2014
MATHEMATICA
p[n_] := p[n] = Select[IntegerPartitions[n], 2*Count[#, _?OddQ] == Count[#, _?EvenQ] &]; Table[p[n], {n, 0, 16}] (* shows partitions *)
TableForm[t] (* partitions, vertical format *)
Table[Length[p[n]], {n, 0, 60}] (* A239004 *)
(* Peter J. C. Moses, Mar 10 2014 *)
b[n_, i_, t_] := b[n, i, t] = If[n==0, If[t==0, 1, 0], If[i<1, 0, b[n, i-1, t] + If[i>n, 0, b[n-i, i, t + If[Mod[i, 2] == 1, 2, -1]]]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Sep 01 2016, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 13 2014
STATUS
approved