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A211373 Sum of median parts of all partitions of n into an odd number of parts.

%I A211373 #21 Aug 20 2021 04:26:51
%S A211373 0,1,2,4,5,9,12,18,24,37,47,68,89,123,160,218,276,370,472,615,778,
%T A211373 1006,1259,1607,2005,2530,3136,3926,4833,6004,7363,9070,11067,13562,
%U A211373 16461,20053,24241,29370,35362,42648,51135,61400,73367,87718,104448,124428,147655
%N A211373 Sum of median parts of all partitions of n into an odd number of parts.
%H A211373 Alois P. Heinz, <a href="/A211373/b211373.txt">Table of n, a(n) for n = 0..1000</a>
%e A211373 a(6) = 12: partitions of 6 into an odd number of parts are [2,1,1,1,1], [2,2,2], [3,2,1], [4,1,1], [6], sum of median parts is 1+2+2+1+6 = 12.
%p A211373 with(combinat):
%p A211373 a:= n-> add(`if`(nops(l)::odd, l[(nops(l)+1)/2], 0), l=partition(n)):
%p A211373 seq(a(n), n=0..40);
%t A211373 a[n_] := Sum[If[OddQ @ Length[l], l[[(Length[l]+1)/2]], 0], {l, IntegerPartitions[n]}];
%t A211373 Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Aug 20 2021, after _Alois P. Heinz_ *)
%Y A211373 Cf. A222044, A222045, A222047, A222048, A268359.
%K A211373 nonn
%O A211373 0,3
%A A211373 _Alois P. Heinz_, Feb 06 2013