

A207779


Largest part plus the number of parts of the nth region of the section model of partitions.


14



2, 4, 6, 3, 9, 4, 12, 3, 6, 4, 17, 4, 7, 5, 22, 3, 6, 4, 10, 6, 5, 30, 4, 7, 5, 11, 4, 8, 6, 39, 3, 6, 4, 10, 6, 5, 15, 5, 9, 7, 6, 52, 4, 7, 5, 11, 4, 8, 6, 17, 6, 5, 11, 8, 7, 67, 3, 6, 4, 10, 6, 5, 15, 5, 9, 7, 6, 22, 4, 8, 6, 13, 5, 10, 8
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Also semiperimeter of the nth region of the geometric version of the section model of partitions. Note that a(n) is easily viewable as the sum of two perpendicular segments with a shared vertex. The horizontal segment has length A141285(n) and the vertical segment has length A194446(n). The difference between these two segments gives A194447(n). See also an illustration in the Links section. For the definition of "region" see A206437.
Also triangle read by rows: T(n,k) = largest part plus the number of parts of the kth region of the last section of the set of partitions of n.


LINKS

Table of n, a(n) for n=1..75.
Omar E. Pol, Illustration of the seven regions of 5


FORMULA

a(n) = A141285(n) + A194446(n).


EXAMPLE

Written as a triangle begins:
2;
4;
6;
3, 9;
4, 12;
3, 6, 4, 17;
4, 7, 5, 22;
3, 6, 4, 10, 6, 5, 30;
4, 7, 5, 11, 4, 8, 6, 39;
3, 6, 4, 10, 6, 5, 15, 5, 9, 7, 6, 52;


CROSSREFS

Row n has length A187219(n). Last term of row n is A133041(n). Where record occur give A000041, n >= 1.
Cf. A002865, A135010, A182699, A182709, A183152, A194436, A194437, A194438, A194439, A194447, A206437.
Sequence in context: A026218 A181473 A181548 * A096665 A064413 A255348
Adjacent sequences: A207776 A207777 A207778 * A207780 A207781 A207782


KEYWORD

nonn,tabf


AUTHOR

Omar E. Pol, Mar 08 2012


STATUS

approved



