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A343801 Total sum of the parts in all partitions counted by A339479(n).

%I A343801 #14 May 02 2022 03:22:15
%S A343801 0,1,5,25,121,583,2789,13287,63149,299697,1421107,6735253,31911985,
%T A343801 151174893,716081551,3391722505,16064368343,76084921797,360353446761,
%U A343801 1706695118265,8083167563465,38283027343193,181313615940197,858725280497117,4067034860337649
%N A343801 Total sum of the parts in all partitions counted by A339479(n).
%H A343801 Alois P. Heinz, <a href="/A343801/b343801.txt">Table of n, a(n) for n = 0..1481</a>
%e A343801 a(3) = 25 = 3+4+6+5+7: [1,1,1], [1,1,2], [1,1,4], [1,2,2], [1,2,4].
%p A343801 b:= proc(n, t) option remember; `if`(n=0, [1, 0],
%p A343801      `if`(t=0, 0, (p-> p+[0, p[2]])(b(n, iquo(t, 2)))+
%p A343801                   (p-> p+[0, p[1]])(b(n-1, t+2))))
%p A343801     end:
%p A343801 a:= n-> b(n, 1)[2]:
%p A343801 seq(a(n), n=0..30);
%t A343801 b[n_, t_] := b[n, t] = If[n == 0, {1, 0}, If[t == 0, {0, 0},
%t A343801      With[{p = b[n, Quotient[t, 2]]}, p + {0, p[[2]]}] +
%t A343801      With[{p = b[n - 1, t + 2]}, p + {0, p[[1]]}]]];
%t A343801 a[n_] := b[n, 1][[2]];
%t A343801 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, May 02 2022, after _Alois P. Heinz_ *)
%Y A343801 Cf. A339479, A343799.
%K A343801 nonn
%O A343801 0,3
%A A343801 _Alois P. Heinz_, Apr 29 2021