A194714 Sum of all odd-indexed parts minus the sum of all even-indexed parts of all partitions of n, with the parts written in nondecreasing order.

1, 2, 3, 4, 5, 8, 9, 14, 18, 26, 32, 48, 57, 82, 102, 138, 169, 230, 278, 370, 450, 584, 709, 914, 1102, 1400, 1692, 2124, 2555, 3186, 3818, 4720, 5649, 6926, 8269, 10078, 11989, 14526, 17249, 20782, 24603, 29508, 34843, 41600, 49008, 58258, 68468, 81098

Offset

1,2

Comments

It appears that A066897 is also another version of this sequence but with the parts written in nonincreasing order.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Example

a(6) = 37 - 29 = 8 because the partitions of 6 written in nondecreasing order are
.
.   6                        =  6
.   3  - 3                   =  0
.   2  - 4                   = -2
.   2  - 2  + 2              =  2
.   1  - 5                   = -4
.   1  - 2  + 3              =  2
.   1  - 1  + 4              =  4
.   1  - 1  + 2 - 2          =  0
.   1  - 1  + 1 - 3          = -2
.   1  - 1  + 1 - 1 + 2      =  2
.   1  - 1  + 1 - 1 + 1 - 1  =  0
----------------------------------
.  20 - 21 + 14 - 7 + 3 - 1  =  8

Crossrefs

Cf. A066897, A135010, A138121, A141285, A194853.

Sequence in context: A163077 A204810 A240080 * A054168 A301464 A354829

Adjacent sequences: A194711 A194712 A194713 * A194715 A194716 A194717

Keyword

nonn

Author

Omar E. Pol, Feb 12 2012

Extensions

More terms from Alois P. Heinz, Feb 12 2012

Status

approved