A253423 Number of (n+2)X(7+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.

5716, 41139, 1399041, 20832926, 187516434, 1042904812, 10608304158, 31966946561, 220223373747, 451565510308, 2982127961746, 5158972747725, 25580058296829, 30372010984513, 146090574735814, 173965238271521

Offset

1,1

Comments

Column 7 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>55.

Empirical for n mod 4 = 0: a(n) = (718127759360/3)*n^4 - (39490511684608/3)*n^3 + (14255146023889861/48)*n^2 - (38862279334406495/12)*n + 14257489007470705 for n>38.

Empirical for n mod 4 = 1: a(n) = (718127759360/3)*n^4 - 12729635040256*n^3 + (13453895148949957/48)*n^2 - (24046237081399511/8)*n + (209379461771811511/16) for n>38.

Empirical for n mod 4 = 2: a(n) = (718127759360/3)*n^4 - (41061416158208/3)*n^3 + (15381923770175941/48)*n^2 - (43432473054074767/12)*n + (65925438070533675/4) for n>38.

Empirical for n mod 4 = 3: a(n) = (718127759360/3)*n^4 - (36618000647168/3)*n^3 + (12344285144411077/48)*n^2 - (63323055557477789/24)*n + (175889901064136459/16) for n>38.

Example

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

Crossrefs

Sequence in context: A025027 A030469 A244163 * A202376 A330208 A252422

Adjacent sequences: A253420 A253421 A253422 * A253424 A253425 A253426

Keyword

nonn

Author

R. H. Hardin, Dec 31 2014

Status

approved