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%I #20 Aug 31 2020 11:41:01
%S 3,7,18,44,82,158,303,507,873,1470,2354,3756,5923,9065,13815,20824,
%T 30853,45365,66210,95415,136696,194414,274057,384136,535219,740559,
%U 1019529,1396212,1901533,2577918,3479291,4673711,6253003,8332767
%N Sum of parts of the n-th subsection of the head of the last section of the set of partitions of any odd integer >= 2n+1.
%C The last section of the set of partitions of 2n+1 contains n subsections.
%C Also first differences of A182737. - Omar E. Pol, Mar 03 2011
%F a(n) = A138880(2n+1) - A138880(2n-1).
%e a(5)=82 because the 5th subsection of the head of the last section of any odd integer >= 11 looks like this:
%e (11 . . . . . . . . . . )
%e ( 6 . . . . . 5 . . . . )
%e ( 7 . . . . . . 4 . . . )
%e ( 8 . . . . . . . 3 . . )
%e ( 4 . . . 4 . . . 3 . . )
%e ( 5 . . . . 3 . . 3 . . )
%e . (2 . )
%e . (2 . )
%e . (2 . )
%e . (2 . )
%e . (2 . )
%e . (2 . )
%e . (2 . )
%e . (2 . )
%e There are 21 parts whose sum is 11+6+5+7+4+8+3+4+4+3+5+3+3+2+2+2+2+2+2+2+2 = 11*6 + 2*8 = 82, so a(5) = 82.
%Y Cf. A135010, A138880, A182737, A182743, A182983, A182993, A182994.
%K nonn
%O 1,1
%A _Omar E. Pol_, Feb 06 2011
%E a(17) corrected and more terms from Omar E. Pol, Mar 03 2011.
%E a(12) corrected by _Georg Fischer_, Aug 31 2020
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