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

1,5

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).

Links

Table of n, a(n) for n=1..13.

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

Example

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.

Crossrefs

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

Sequence in context: A358055 A011842 A000094 * A327380 A330378 A058578

Adjacent sequences: A182374 A182375 A182376 * A182378 A182379 A182380

Keyword

nonn,more

Author

Omar E. Pol, Apr 29 2012

Status

approved