A182377 Total sum of positive ranks of all regions in the last shell of n.

0, 0, 0, 1, 2, 5, 8, 14, 21, 32, 45, 67, 91

Offset: 1

Author

Omar E. Pol, Apr 29 2012

Keywords

• nonn
• more

Comments

The rank of a region of n is the largest part minus the number of parts. For the definition of "region of n" see A206437. For the definition of "last shell of n" see A135010.

a(n) is also the sum of positive integers in row n of triangle A194447. First differs from A000094 at a(12).

Examples

			For n = 7 the last shell of 7 contains four regions: [3],[5,2],[4],[7,3,2,2,1,1,1,1,1,1,1,1,1,1,1] so we have:
----------------------------------------------------------
.        Largest    Number
Region     part    of parts    Rank
----------------------------------------------------------
.  1        3         1          2
.  2        5         2          3
.  3        4         1          3
.  4        7        15         -8
.
The sum of positive ranks is a(7) = 2 + 3 + 3 = 8.
		

Links

• Omar E. Pol, Illustration of the seven regions of 5

Crossrefs

Cf. A000094, A135010, A138121, A182699, A182709, A183152, A186114, A187219, A194436-A194439, A194447-A194448, A196025, A206437, A209616.