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%I #12 Sep 01 2016 08:13:42
%S 1,0,0,0,0,1,0,2,0,4,1,6,2,9,5,13,9,18,17,25,28,35,46,49,70,70,107,
%T 101,156,145,227,210,321,303,453,436,628,622,868,884,1187,1243,1619,
%U 1738,2192,2410,2960,3317,3977,4532,5331,6154,7117,8298,9477,11129
%N Number of partitions of n having twice as many even parts as odd.
%H Alois P. Heinz, <a href="/A239004/b239004.txt">Table of n, a(n) for n = 0..1000</a>
%e a(11) counts these 6 partitions: 821, 722, 641, 632, 542, 443.
%p b:= proc(n, i, t) option remember;
%p `if`(n=0, `if`(t=0, 1, 0), `if`(i<1, 0, b(n, i-1, t)+
%p `if`(i>n, 0, b(n-i, i, t+`if`(irem(i, 2)=1, 2, -1)))))
%p end:
%p a:= n-> b(n$2, 0):
%p seq(a(n), n=0..60); # _Alois P. Heinz_, Mar 14 2014
%t p[n_] := p[n] = Select[IntegerPartitions[n], 2*Count[#, _?OddQ] == Count[#, _?EvenQ] &]; Table[p[n], {n, 0, 16}] (* shows partitions *)
%t TableForm[t] (* partitions, vertical format *)
%t Table[Length[p[n]], {n, 0, 60}] (* A239004 *)
%t (* _Peter J. C. Moses_, Mar 10 2014 *)
%t 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_ *)
%Y Cf. A239258.
%K nonn,easy
%O 0,8
%A _Clark Kimberling_, Mar 13 2014
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