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A253417 Number of (n+2)X(1+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
17, 56, 257, 642, 1581, 2389, 5716, 7691, 11429, 13229, 25870, 30605, 39701, 42941, 73200, 81815, 99709, 104837, 163706, 177321, 208349, 215813, 316972, 336707, 386101, 396349, 556166, 583141, 657029, 670509, 908040, 943375, 1048781, 1065941 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 1 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>21.

Empirical for n mod 4 = 0: a(n) = (7/12)*n^4 + 9*n^3 + (563/12)*n^2 - (745/2)*n + 671 for n>4.

Empirical for n mod 4 = 1: a(n) = (7/12)*n^4 + 9*n^3 + (479/12)*n^2 - (643/2)*n + 701 for n>4.

Empirical for n mod 4 = 2: a(n) = (7/12)*n^4 + (20/3)*n^3 + (365/12)*n^2 - (1058/3)*n + 1214 for n>4.

Empirical for n mod 4 = 3: a(n) = (7/12)*n^4 + (34/3)*n^3 + (509/12)*n^2 - (928/3)*n + 515 for n>4.

EXAMPLE

Some solutions for n=2

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

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

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

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

Knight distance matrix for n=2

..0..3..2

..3..4..1

..2..1..4

..5..2..3

CROSSREFS

Sequence in context: A072895 A097059 A253424 * A117390 A141841 A146682

Adjacent sequences:  A253414 A253415 A253416 * A253418 A253419 A253420

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 31 2014

STATUS

approved

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Last modified April 23 18:45 EDT 2017. Contains 285329 sequences.