OFFSET
2,1
COMMENTS
The subset of nodes is contained in the top left-hand quarter of the rectangle and has nodal dimensions floor((n+1)/2) and 1 to capture all geometrically distinct counts. The quarter-rectangle is read by rows. The irregular array of numbers is:
....k.....1..2..3..4..5..6..7..8..9.10
..n
..2.......2
..3.......5..0
..4......10..0
..5......18..0..0
..6......31..0..0
..7......52..0..0..0
..8......86..0..0..0
..9.....141..0..0..0..0
.10.....230..0..0..0..0
.11.....374..0..0..0..0..0
.12.....607..0..0..0..0..0
.13.....984..0..0..0..0..0..0
.14....1594..0..0..0..0..0..0
.15....2581..0..0..0..0..0..0..0
.16....4178..0..0..0..0..0..0..0
.17....6762..0..0..0..0..0..0..0..0
.18...10943..0..0..0..0..0..0..0..0
.19...17708..0..0..0..0..0..0..0..0..0
.20...28654..0..0..0..0..0..0..0..0..0
where k indicates the position of the end node in the quarter-rectangle. For each n, the maximum value of k is floor((n+1)/2). Reading this array by rows gives the sequence.
LINKS
FORMULA
Let T(n,k) denote an element of the irregular array then it appears that T(n,k) = A000045(n+3) - 3, n >= 2, k = 1 and T(n,k) = 0, n >= 2, k >= 2.
EXAMPLE
When n = 2, the number of times (NT) each node in the rectangle is the end node (EN) of a complete non-self-adjacent simple path is
EN 0 1
2 3
NT 2 2
2 2
To limit duplication, only the top left-hand corner 2 is stored in the sequence, i.e. T(2,1) = 2.
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Christopher Hunt Gribble, Jul 04 2012
STATUS
approved