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Number of partitions of n with equal number of parts congruent to each of 0 and 2 (mod 3).
1

%I #15 Sep 07 2020 05:59:54

%S 1,1,1,1,2,3,3,4,7,8,10,14,18,22,29,37,47,58,73,91,113,140,174,211,

%T 260,319,386,468,572,687,828,998,1197,1431,1714,2041,2430,2887,3424,

%U 4051,4792,5651,6659,7829,9199,10786,12631,14770,17258,20120,23444,27278

%N Number of partitions of n with equal number of parts congruent to each of 0 and 2 (mod 3).

%H Alois P. Heinz, <a href="/A035535/b035535.txt">Table of n, a(n) for n = 0..1000</a>

%p b:= proc(n, i, c) option remember; `if`(n=0,

%p `if`(c=0, 1, 0), `if`(i<1, 0, b(n, i-1, c)+

%p b(n-i, min(n-i, i), c+[1, 0, -1][1+irem(i, 3)])))

%p end:

%p a:= n-> b(n$2, 0):

%p seq(a(n), n=0..70); # _Alois P. Heinz_, Sep 04 2020

%t equalQ[partit_] := Total[Switch[Mod[#, 3], 0, -1, 1, 0, 2, 1]& /@ partit] == 0; a[n_] := Select[IntegerPartitions[n] , equalQ] // Length; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 51}] (* _Jean-François Alcover_, Dec 07 2016 *)

%K nonn

%O 0,5

%A _Olivier Gérard_

%E More terms from _David W. Wilson_