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A253418 Number of (n+2)X(2+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
56, 131, 1087, 2827, 10411, 15803, 41139, 52297, 111085, 130089, 241833, 270699, 459463, 500207, 794663, 849301, 1282729, 1353277, 1963565, 2052039, 2881683, 2990099, 4086203, 4216577, 5630853, 5785201, 7573969, 7754307, 9978495 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 2 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-2) -4*a(n-3) -6*a(n-4) +6*a(n-5) +4*a(n-6) -4*a(n-7) -a(n-8) +a(n-9) for n>15.

Empirical for n mod 2 = 0: a(n) = 12*n^4 + (46/3)*n^3 + (577/4)*n^2 - (17195/6)*n + 8989 for n>6.

Empirical for n mod 2 = 1: a(n) = 12*n^4 + (190/3)*n^3 + (41/4)*n^2 - (7123/3)*n + (26887/4) for n>6.

EXAMPLE

Some solutions for n=2

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

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

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

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

Knight distance matrix for n=2

..0..3..2..5

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

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

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

CROSSREFS

Sequence in context: A030443 A135803 A048452 * A204840 A204833 A121736

Adjacent sequences:  A253415 A253416 A253417 * A253419 A253420 A253421

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 31 2014

STATUS

approved

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Last modified January 19 17:45 EST 2019. Contains 319309 sequences. (Running on oeis4.)