OFFSET
1,1
COMMENTS
Column 3 of A253119
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = a(n-1) +8*a(n-4) -8*a(n-5) -28*a(n-8) +28*a(n-9) +56*a(n-12) -56*a(n-13) -70*a(n-16) +70*a(n-17) +56*a(n-20) -56*a(n-21) -28*a(n-24) +28*a(n-25) +8*a(n-28) -8*a(n-29) -a(n-32) +a(n-33) for n>48.
Empirical for n mod 4 = 0: a(n) = (48128/315)*n^8 - (70784/45)*n^7 + (1613986/45)*n^6 - (408827287/360)*n^5 + (656806290529/46080)*n^4 - (417508867243/5760)*n^3 + (1340641181597/20160)*n^2 + (68326310189/120)*n - 1314231925 for n>15.
Empirical for n mod 4 = 1: a(n) = (48128/315)*n^8 - (399232/315)*n^7 + (494198/15)*n^6 - (391895399/360)*n^5 + (200444821003/15360)*n^4 - (719258439109/11520)*n^3 + (8134684965509/161280)*n^2 + (12687388527967/26880)*n - (1104560946555/1024) for n>15.
Empirical for n mod 4 = 2: a(n) = (48128/315)*n^8 - (784256/315)*n^7 + (254546/5)*n^6 - (494044999/360)*n^5 + (99930960601/5120)*n^4 - (787756612561/5760)*n^3 + (17328260184551/40320)*n^2 - (780223082251/3360)*n - (71148317231/64) for n>15.
Empirical for n mod 4 = 3: a(n) = (48128/315)*n^8 - (110464/315)*n^7 + (516898/45)*n^6 - (54346123/72)*n^5 + (321821523169/46080)*n^4 + (153162748967/11520)*n^3 - (67343538926807/161280)*n^2 + (8549722002355/5376)*n - (1254021550131/1024) for n>15.
EXAMPLE
Some solutions for n=3:
..0..2..2..2..2....0..2..2..1..2....0..1..1..1..0....0..2..0..1..1
..2..3..1..2..2....2..2..1..2..2....1..2..0..0..1....1..2..1..1..1
..2..1..3..2..1....1..1..2..2..1....1..0..2..1..1....1..0..2..1..1
..2..2..2..2..2....2..1..2..1..2....1..1..1..1..1....1..1..1..1..1
..2..2..1..2..3....2..2..1..1..2....0..1..1..1..2....0..1..0..1..2
Knight distance matrix for n=3:
..0..3..2..3..2
..3..4..1..2..3
..2..1..4..3..2
..3..2..3..2..3
..2..3..2..3..4
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 27 2014
STATUS
approved