A352505 Sum of all parts of all partitions of n into an even number of consecutive parts.

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, 0, 29, 30, 31, 0, 66, 34, 35, 36, 37, 38, 78, 0, 41, 42, 43, 44, 90, 46, 47, 0, 49, 50, 102, 52, 53, 54, 110, 0, 114, 58, 59, 60, 61, 62, 126, 0, 130, 66, 67, 68, 138, 70, 71, 0

Offset

1,3

Links

Table of n, a(n) for n=1..72.

Formula

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

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

Example

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.

Crossrefs

Indices of zero terms give A082662.

Indices of nonzero terms give A281005.

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

Sequence in context: A347347 A071649 A341310 * A210524 A325961 A049283

Adjacent sequences: A352502 A352503 A352504 * A352506 A352507 A352508

Keyword

nonn

Author

Omar E. Pol, Mar 19 2022

Status

approved