login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A253113 Number of (n+2)X(2+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
272, 920, 6334, 28600, 139760, 502272, 2259097, 5670421, 21399557, 39120366, 120865988, 183106294, 479657064, 649963111, 1500762543, 1895383751, 3973980189, 4787211558, 9308563998, 10844855216, 19852566186, 22566185885 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 2 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>29.

Empirical for n mod 2 = 0: a(n) = (8/45)*n^8 + (1504/315)*n^7 + (3571/45)*n^6 - (84011/45)*n^5 + (5095469/1440)*n^4 + (27027629/360)*n^3 - (17188069/180)*n^2 - (433790313/140)*n + 11000595 for n>12.

Empirical for n mod 2 = 1: a(n) = (8/45)*n^8 + (1952/315)*n^7 + (301/3)*n^6 - (70897/45)*n^5 - (1084059/160)*n^4 + (23349461/180)*n^3 - (6792595/144)*n^2 - (509001211/140)*n + (327336053/32) for n>12.

EXAMPLE

Some solutions for n=4:

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

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

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

..2..2..2..2....2..2..2..1....2..1..2..2....2..1..2..2....2..2..2..1

..2..2..2..2....1..2..2..2....2..2..1..2....1..2..2..1....2..2..2..2

..2..2..3..3....3..2..2..3....2..2..2..3....2..2..2..2....2..2..2..3

Knight distance matrix for n=4:

..0..3..2..5

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

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

..3..2..3..2

..2..3..2..3

..3..4..3..4

CROSSREFS

Sequence in context: A316374 A306134 A317269 * A234884 A158587 A304417

Adjacent sequences:  A253110 A253111 A253112 * A253114 A253115 A253116

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 27 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 29 03:50 EDT 2022. Contains 357082 sequences. (Running on oeis4.)