A162934 Shift sequence A162932 twice then subtract from the original sequence.

1, 0, 0, 1, 0, 0, 2, 0, 0, 3, 1, 0, 4, 2, 2, 5, 3, 4, 9, 5, 6, 13, 11, 10, 19, 17, 19, 28, 27, 31, 44, 41, 49, 66, 68, 74, 98, 104, 118, 145, 157, 178, 220, 234, 268, 322, 354, 397, 473, 521, 591, 686, 765, 863, 1003, 1107, 1254, 1444, 1609

Offset

6,7

Comments

From Alford Arnold, Dec 17 2009: (Start)

at N=24, six of the partitions can be associated with the sixth row of this

triangular array:

333

444 3333

555 4443 33333

666 5553 44433 333333

777 6663 55533 444333 3333333

888 7773 66633 555333 4443333 33333333

The other three partitions are new; and hence on their first row, so 6*1+1*3=9

In a similar manner, the 44 cases at N=36 can be computed using the array row

numbers and the number of applicable partitions. Thus we have:

(10, 5, 3, 2, 1) times (1, 3, 2, 3, 7) providing 10+15+6+6+7 = 44 cases. (End)

Links

Table of n, a(n) for n=6..64.

Example

For n= 24 the sequence counts these nine partitions: 888 7773 66633 55554 555333 4443333 6666 444444 33333333

Crossrefs

Cf. A000041 A002865 A053445 A162932

Sequence in context: A309577 A029301 A263414 * A303908 A351592 A082660

Adjacent sequences: A162931 A162932 A162933 * A162935 A162936 A162937

Keyword

nonn

Author

Alford Arnold, Aug 05 2009, Aug 06 2009

Extensions

More terms from Alford Arnold, Dec 17 2009

Added more terms, Joerg Arndt, Jul 16 2015

Status

approved