A284475 Total number of parts in all partitions of n into equal parts, minus the total number of parts in all partitions of n into consecutive parts.

0, 2, 1, 6, 3, 8, 5, 14, 7, 13, 9, 24, 11, 19, 13, 30, 15, 31, 17, 36, 20, 31, 21, 56, 23, 37, 28, 48, 27, 59, 29, 62, 36, 49, 33, 79, 35, 55, 44, 84, 39, 81, 41, 75, 52, 67, 45, 120, 47, 83, 60, 89, 51, 103, 54, 112, 68, 85, 57, 151, 59, 91, 76, 126, 66, 125, 65, 117, 84, 127, 69, 182, 71, 109, 97, 131, 75, 148

Offset

1,2

Comments

Observation: at least for the first 78 terms of this sequence the values of n where a(n) = n - 2 coincide with the odd numbers of A082664.

Links

Table of n, a(n) for n=1..78.

Formula

Conjecture: a(n) = A000203(n) - A204217(n).

a(2^k) = A000918(k+1), k>=0.

Example

For n = 10 the partitions of 10 into equal parts are [10], [5, 5], [2, 2, 2, 2, 2] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]. The total number of parts is 18. On the other hand, the partitions of 10 into consecutive parts are [10] and [4, 3, 2, 1]. The total number of parts is 5, so a(10) = 18 - 5 = 13.

Crossrefs

Cf. A000203, A000918, A082647, A082664, A204217, A285914.

Sequence in context: A126265 A293182 A124441 * A353660 A285355 A316605

Adjacent sequences: A284472 A284473 A284474 * A284476 A284477 A284478

Keyword

nonn

Author

Omar E. Pol, May 03 2017

Status

approved