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A206433 Total number of odd parts in the last section of the set of partitions of n.

%I A206433 #31 Apr 30 2023 22:19:58
%S A206433 1,1,3,3,7,9,15,19,32,40,60,78,111,143,200,252,343,437,576,728,952,
%T A206433 1190,1531,1911,2426,3008,3788,4664,5819,7143,8830,10780,13255,16095,
%U A206433 19661,23787,28881,34795,42051,50445,60675,72547,86859,103481,123442,146548
%N A206433 Total number of odd parts in the last section of the set of partitions of n.
%C A206433 From _Omar E. Pol_, Apr 07 2023: (Start)
%C A206433 Convolution of A002865 and A001227.
%C A206433 a(n) is also the total number of odd divisors of the terms in the n-th row of the triangle A336811.
%C A206433 a(n) is also the number of odd terms in the n-th row of the triangle A207378.
%C A206433 a(n) is also the number of odd terms in the n-th row of the triangle A336812. (End)
%H A206433 Alois P. Heinz, <a href="/A206433/b206433.txt">Table of n, a(n) for n = 1..1000</a>
%p A206433 b:= proc(n, i) option remember; local f, g;
%p A206433       if n=0 or i=1 then [1, n]
%p A206433     else f:= b(n, i-1); g:= `if`(i>n, [0, 0], b(n-i, i));
%p A206433          [f[1]+g[1], f[2]+g[2]+ (i mod 2)*g[1]]
%p A206433       fi
%p A206433     end:
%p A206433 a:= n-> b(n, n)[2] -b(n-1, n-1)[2]:
%p A206433 seq(a(n), n=1..50);  # _Alois P. Heinz_, Mar 22 2012
%t A206433 b[n_, i_] := b[n, i] = Module[{f, g}, If[n==0 || i==1, {1, n}, f = b[n, i-1]; g = If[i>n, {0, 0}, b[n-i, i]]; {f[[1]]+g[[1]], f[[2]]+g[[2]] + Mod[i, 2]*g[[1]]}]]; a[n_] := b[n, n][[2]]-b[n-1, n-1][[2]]; Table[a[n], {n, 1, 50}] (* _Jean-François Alcover_, Feb 16 2017, after _Alois P. Heinz_ *)
%Y A206433 Partial sums give A066897.
%Y A206433 Cf. A001227, A002865, A006128, A135010, A138121, A138137, A182703, A206434, A206435, A206436, A207378, A336811, A336812.
%K A206433 nonn
%O A206433 1,3
%A A206433 _Omar E. Pol_, Feb 12 2012
%E A206433 More terms from _Alois P. Heinz_, Mar 22 2012