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

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

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.

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