A352257 Sum of all parts of all partitions of n into an odd number of consecutive parts.

1, 2, 3, 4, 5, 12, 7, 8, 18, 10, 11, 24, 13, 14, 45, 16, 17, 36, 19, 40, 42, 22, 23, 48, 50, 26, 54, 56, 29, 90, 31, 32, 66, 34, 105, 72, 37, 38, 78, 80, 41, 126, 43, 44, 180, 46, 47, 96, 98, 100, 102, 52, 53, 162, 110, 112, 114, 58, 59, 180, 61, 62, 252, 64, 130, 198

Offset

1,2

Comments

a(n) is n times the number of partitions of n into an odd number of consecutive parts.

Links

Table of n, a(n) for n=1..66.

Formula

a(n) = n*A082647(n).

a(n) = A245579(n) - A352505(n). - Omar E. Pol, Mar 19 2022

Example

For n = 15 the partitions of 15 into an odd number of consecutive parts are [15], [6, 5, 4] and [5, 4, 3, 2, 1], so a(15) = 15 + 6 + 5 + 4 + 5 + 4 + 3 + 2 + 1 = 15*3 = 45.

Prog

(PARI) a(n) = my(q = sqrt(2*n)); n*sumdiv(n, d, (d%2) && (d < q)); \\ Michel Marcus, Mar 11 2022; after A082647

Crossrefs

Row sums of A352499.

Cf. A066186, A082647, A237048, A245579, A286000, A286001, A299765, A351824, A352505.

Sequence in context: A135323 A052106 A064446 * A225607 A227987 A261863

Adjacent sequences: A352254 A352255 A352256 * A352258 A352259 A352260

Keyword

nonn

Author

Omar E. Pol, Mar 09 2022

Status

approved