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 A239004 Number of partitions of n having twice as many even parts as odd. 2
 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, 101, 156, 145, 227, 210, 321, 303, 453, 436, 628, 622, 868, 884, 1187, 1243, 1619, 1738, 2192, 2410, 2960, 3317, 3977, 4532, 5331, 6154, 7117, 8298, 9477, 11129 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A239258. Sequence in context: A056737 A289144 A008797 * A168036 A217930 A305371 Adjacent sequences:  A239001 A239002 A239003 * A239005 A239006 A239007 KEYWORD nonn,easy AUTHOR Clark Kimberling, Mar 13 2014 STATUS approved

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Last modified July 24 06:04 EDT 2021. Contains 346273 sequences. (Running on oeis4.)