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A253421 Number of (n+2)X(5+2) nonnegative integer arrays with all values the knight distance from the upper left minus as much as 1, with successive minimum path knight move differences either 0 or +1, and any unreachable value zero. 1
1581, 10411, 215037, 1432500, 9787192, 31393746, 187516434, 402193875, 1885771797, 2402676252, 10791372467, 13668072759, 29495644141, 31712757323, 83214252197, 92712352801, 154900321588, 160193732925, 330016199502 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 5 of A253424.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = a(n-1) +4*a(n-4) -4*a(n-5) -6*a(n-8) +6*a(n-9) +4*a(n-12) -4*a(n-13) -a(n-16) +a(n-17) for n>35.

Empirical for n mod 4 = 0: a(n) = (36118528/3)*n^4 - (1157303200/3)*n^3 + (520897460059/96)*n^2 - (927400346113/24)*n + 113007591457 for n>18.

Empirical for n mod 4 = 1: a(n) = (36118528/3)*n^4 - (1103125408/3)*n^3 + (483238622299/96)*n^2 - (1699831438517/48)*n + (3301652661093/32) for n>18.

Empirical for n mod 4 = 2: a(n) = (36118528/3)*n^4 - (1247599520/3)*n^3 + (600461819995/96)*n^2 - (567913877425/12)*n + (1175858264163/8) for n>18.

Empirical for n mod 4 = 3: a(n) = (36118528/3)*n^4 - 337609696*n^3 + (402428173147/96)*n^2 - (426295607213/16)*n + (2227476245245/32) for n>18.

EXAMPLE

Some solutions for n=2

..0..2..2..3..2..2..3....0..2..1..3..2..3..3....0..2..2..2..2..2..3

..2..3..1..2..2..3..2....2..3..1..2..2..3..2....2..3..1..2..3..3..2

..1..1..3..2..2..2..3....2..1..3..2..2..2..3....1..1..3..2..1..3..3

..4..2..2..1..2..3..3....4..1..3..2..2..3..3....4..1..2..2..3..3..2

Knight distance matrix for n=2

..0..3..2..3..2..3..4

..3..4..1..2..3..4..3

..2..1..4..3..2..3..4

..5..2..3..2..3..4..3

CROSSREFS

Sequence in context: A223399 A210294 A203961 * A023082 A216064 A182409

Adjacent sequences:  A253418 A253419 A253420 * A253422 A253423 A253424

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 31 2014

STATUS

approved

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Last modified May 7 09:41 EDT 2021. Contains 343649 sequences. (Running on oeis4.)