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%I #21 May 23 2012 09:38:49
%S 1,2,3,4,5,8,9,14,18,26,32,48,57,82,102,138,169,230,278,370,450,584,
%T 709,914,1102,1400,1692,2124,2555,3186,3818,4720,5649,6926,8269,10078,
%U 11989,14526,17249,20782,24603,29508,34843,41600,49008,58258,68468,81098
%N Sum of all odd-indexed parts minus the sum of all even-indexed parts of all partitions of n, with the parts written in nondecreasing order.
%C It appears that A066897 is also another version of this sequence but with the parts written in nonincreasing order.
%H Alois P. Heinz, <a href="/A194714/b194714.txt">Table of n, a(n) for n = 1..1000</a>
%e a(6) = 37 - 29 = 8 because the partitions of 6 written in nondecreasing order are
%e .
%e . 6 = 6
%e . 3 - 3 = 0
%e . 2 - 4 = -2
%e . 2 - 2 + 2 = 2
%e . 1 - 5 = -4
%e . 1 - 2 + 3 = 2
%e . 1 - 1 + 4 = 4
%e . 1 - 1 + 2 - 2 = 0
%e . 1 - 1 + 1 - 3 = -2
%e . 1 - 1 + 1 - 1 + 2 = 2
%e . 1 - 1 + 1 - 1 + 1 - 1 = 0
%e ----------------------------------
%e . 20 - 21 + 14 - 7 + 3 - 1 = 8
%Y Cf. A066897, A135010, A138121, A141285, A194853.
%K nonn
%O 1,2
%A _Omar E. Pol_, Feb 12 2012
%E More terms from _Alois P. Heinz_, Feb 12 2012