A253115 Number of (n+2)X(4+2) nonnegative integer arrays with all values the knight distance from the upper left minus as much as 2, with successive minimum path knight move differences either 0 or +1, and any unreachable value zero.

4619, 28600, 426571, 3950239, 28256241, 201911670, 1873418602, 7421334529, 54446797689, 133685068828, 745867325532, 1354111174816, 5818864244979, 8824640573225, 30688212938784, 41602065842866, 122867434214623

Offset

1,1

Comments

Column 4 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-2) -8*a(n-3) -28*a(n-4) +28*a(n-5) +56*a(n-6) -56*a(n-7) -70*a(n-8) +70*a(n-9) +56*a(n-10) -56*a(n-11) -28*a(n-12) +28*a(n-13) +8*a(n-14) -8*a(n-15) -a(n-16) +a(n-17) for n>37.

Empirical for n mod 2 = 0: a(n) = (17563648/63)*n^8 - (753270784/45)*n^7 + (4959576064/9)*n^6 - (567642929152/45)*n^5 + (1853435878336/9)*n^4 - (104612636971216/45)*n^3 + (119980082024136/7)*n^2 - (2219288775756637/30)*n + 140910866347888 for n>20.

Empirical for n mod 2 = 1: a(n) = (17563648/63)*n^8 - (1523449856/105)*n^7 + (19261530112/45)*n^6 - (136247502848/15)*n^5 + (1247647337408/9)*n^4 - (21746003662832/15)*n^3 + (3075715875376376/315)*n^2 - (2653723481992701/70)*n + (127386927252109/2) for n>20.

Example

Some solutions for n=2:
..0..2..1..2..2..2....0..2..1..2..1..2....0..2..1..2..1..2....0..1..1..1..1..1
..2..3..1..1..2..2....2..2..1..1..2..2....1..2..0..1..1..2....2..2..1..1..2..2
..2..0..2..2..1..2....1..1..2..2..2..2....1..0..2..1..1..1....1..0..2..2..1..1
..3..2..2..1..2..3....3..2..2..2..1..3....3..1..2..0..2..2....3..1..2..1..2..2
Knight distance matrix for n=2:
..0..3..2..3..2..3
..3..4..1..2..3..4
..2..1..4..3..2..3
..5..2..3..2..3..4

Crossrefs

Sequence in context: A265926 A365483 A260054 * A189983 A295431 A338337

Adjacent sequences: A253112 A253113 A253114 * A253116 A253117 A253118

Keyword

nonn

Author

R. H. Hardin, Dec 27 2014

Status

approved