A253418 - OEIS

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.

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

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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: A135803 A048452 A306935 * A204840 A204833 A121736

Adjacent sequences: A253415 A253416 A253417 * A253419 A253420 A253421

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 31 2014

STATUS

approved