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

Author

Omar E. Pol, Feb 12 2012

Keywords

• nonn

Comments

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

Examples

			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
		

Links

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

Crossrefs

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

Extensions

More terms from Alois P. Heinz, Feb 12 2012