login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Sum of all parts of all partitions of n into an even number of consecutive parts.
3

%I #15 Apr 23 2022 09:44:42

%S 0,0,3,0,5,0,7,0,9,10,11,0,13,14,15,0,17,18,19,0,42,22,23,0,25,26,54,

%T 0,29,30,31,0,66,34,35,36,37,38,78,0,41,42,43,44,90,46,47,0,49,50,102,

%U 52,53,54,110,0,114,58,59,60,61,62,126,0,130,66,67,68,138,70,71,0

%N Sum of all parts of all partitions of n into an even number of consecutive parts.

%F a(n) = n*A131576(n).

%F a(n) = A245579(n) - A352257(n).

%e For n = 21 the partitions of 21 into an even number of consecutive parts are [11, 10] and [6, 5, 4, 3, 2, 1], so a(21) = 11 + 10 + 6 + 5 + 4 + 3 + 2 + 1 = 21*2 = 42.

%Y Indices of zero terms give A082662.

%Y Indices of nonzero terms give A281005.

%Y Cf. A066186, A131576, A245579, A285891, A286000, A286001, A299765, A352257.

%K nonn

%O 1,3

%A _Omar E. Pol_, Mar 19 2022