A253117 Number of (n+2)X(6+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.

34786, 502272, 11529235, 201911670, 3518586637, 40022802662, 638441329329, 7166392767013, 68323597331510, 307062940433405, 4214839734514057, 9577612840865990, 77191247728672767, 130867110971414685

Offset

1,1

Comments

Column 6 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>65.

Empirical for n mod 2 = 0: a(n) = (319253509046272/315)*n^8 - (2945579436998656/21)*n^7 + (417387011505258496/45)*n^6 - (5680344823516484096/15)*n^5 + (1861327919333148550921/180)*n^4 - (575420368345587182792/3)*n^3 + (164089389444136785259229/70)*n^2 - (3604156184637146154909821/210)*n + 57374514750466974203474 for n>48.

Empirical for n mod 2 = 1: a(n) = (319253509046272/315)*n^8 - (5947094783229952/45)*n^7 + (373238238302830592/45)*n^6 - (14547581331407468032/45)*n^5 + (1523828668871093157641/180)*n^4 - (6800467172678093885353/45)*n^3 + (561465751276267695242221/315)*n^2 - (378712331403727320080417/30)*n + (163612095136090005773229/4) for n>48.

Example

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

Crossrefs

Sequence in context: A103911 A185472 A116016 * A236591 A236727 A233815

Adjacent sequences: A253114 A253115 A253116 * A253118 A253119 A253120

Keyword

nonn

Author

R. H. Hardin, Dec 27 2014

Status

approved