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

Author

Omar E. Pol, Mar 19 2022

Keywords

• nonn

Examples

			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.

Formula

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

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