T(n,k)=Number of lower triangular nXn n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any diagonal or antidiagonal neighbor, and containing the value n(n+1)/2-k-1

editing

approved

R. H. Hardin, <a href="/A211963/b211963.txt">Table of n, a(n) for n = 1..85</a>

allocated for R. H. Hardin

T(n,k)=Number of lower triangular nXn arrays colored with integers 0 upwards introduced in row major order, with no element equal to any diagonal or antidiagonal neighbor, and containing the value n(n+1)/2-k-1

0, 0, 3, 0, 3, 12, 0, 0, 43, 37, 0, 0, 65, 499, 90, 0, 0, 67, 3146, 3304, 186, 0, 0, 67, 10112, 64705, 15021, 343, 0, 0, 0, 17947, 743866, 695587, 53038, 582, 0, 0, 0, 21062, 5225620, 20556897, 4904333, 156458, 927, 0, 0, 0, 21348, 22803273, 408588191, 303369413

1,3

Table starts

...0......0........0..........0............0............0..............0

...3......3........0..........0............0............0..............0

..12.....43.......65.........67...........67............0..............0

..37....499.....3146......10112........17947........21062..........21348

..90...3304....64705.....743866......5225620.....22803273.......62515357

.186..15021...695587...20556897....408588191...5612346726....53970698094

.343..53038..4904333..303369413..13307423101.428253737962.10321456003638

.582.156458.25825865.2935224783.244159057556

Some solutions for n=4 k=4

..0........0........0........0........0........0........0........0

..0.1......1.2......1.1......0.1......1.2......1.2......1.2......1.2

..2.2.3....0.3.3....2.3.4....2.3.0....3.0.0....0.3.4....0.3.1....3.4.5

..4.1.5.6..4.5.6.1..1.3.2.5..4.3.5.1..4.5.5.3..0.3.0.5..4.5.5.5..6.1.3.1

allocated

nonn,tabl

R. H. Hardin Apr 26 2012

approved

editing

allocated for R. H. Hardin

allocated

approved