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A253112 Number of (n+2)X(1+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. 1
53, 272, 1342, 4619, 14541, 34786, 113891, 233392, 525617, 853971, 2327441, 3609337, 6243433, 8189113, 18881723, 25291483, 37714007, 44777219, 90840301, 112309445, 153843349, 173399285, 320621751, 377531207, 490093227, 535756183 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 1 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>43.

Empirical for n mod 4 = 0: a(n) = (1/2880)*n^8 + (1/35)*n^7 + (169/160)*n^6 + (91/12)*n^5 - (170437/960)*n^4 - (4291/60)*n^3 + (547067/45)*n^2 - (1847017/42)*n - 22525 for n>10.

Empirical for n mod 4 = 1: a(n) = (1/2880)*n^8 + (1/35)*n^7 + (1493/1440)*n^6 + (871/120)*n^5 - (506711/2880)*n^4 + (3067/30)*n^3 + (1371401/120)*n^2 - (11084513/210)*n + (371127/16) for n>10.

Empirical for n mod 4 = 2: a(n) = (1/2880)*n^8 + (13/504)*n^7 + (85/96)*n^6 + (2389/720)*n^5 - (50539/320)*n^4 + (93863/144)*n^3 + (142985/18)*n^2 - (26157409/420)*n + (399767/4) for n>10.

Empirical for n mod 4 = 3: a(n) = (1/2880)*n^8 + (79/2520)*n^7 + (187/160)*n^6 + (7409/720)*n^5 - (190777/960)*n^4 - (235699/720)*n^3 + (5757523/360)*n^2 - (52286503/840)*n + (146121/16) for n>10

EXAMPLE

Some solutions for n=4:

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

..3..2..1....2..4..1....2..3..1....1..2..1....1..2..0....2..2..1....1..2..0

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

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

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

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

Knight distance matrix for n=4:

..0..3..2

..3..4..1

..2..1..4

..3..2..3

..2..3..2

..3..4..3

CROSSREFS

Sequence in context: A140851 A337428 A253119 * A211146 A155700 A108878

Adjacent sequences: A253109 A253110 A253111 * A253113 A253114 A253115

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 27 2014

STATUS

approved

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Last modified December 1 05:02 EST 2022. Contains 358454 sequences. (Running on oeis4.)