OFFSET
1,1
COMMENTS
Table starts
....4......7......10........13.........16.........19..........22...........25
...12.....53.....152.......345........676.......1197........1968.........3057
...16.....90.....281.......673.......1356.......2452........4083.........6409
...40....393....2058......7257......19990......46945.......98124.......187593
...64....952....6515.....28428......92041.....246003......570578......1191085
..144...3323...32166....184145.....764836....2521335.....7036012.....17264207
..256...9205..119317....866944....4373134...16987236....54817908....153203700
..544..29445..517390...4737473...29088446..134079743...503679532...1613885479
.1024..85717.2015982..23297196..172527610..932611547..4023378619..14596031060
.2112.264455.8326770.120376601.1072084446.6789960255.33615995160.137794713707
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..221
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1) +2*a(n-2) -4*a(n-3)
k=2: [order 16]
k=3: [order 63] for n>64
Empirical for row n:
n=1: a(n) = 3*n + 1
n=2: a(n) = (1/3)*n^4 + (8/3)*n^3 + (14/3)*n^2 + (10/3)*n + 1
n=3: a(n) = 3*a(n-1) -a(n-2) -5*a(n-3) +5*a(n-4) +a(n-5) -3*a(n-6) +a(n-7)
n=4: [order 15]
Empirical quasipolynomials for row n:
n=3: polynomial of degree 4 plus a quasipolynomial of degree 1 with period 2
n=4: polynomial of degree 6 plus a quasipolynomial of degree 3 with period 3
EXAMPLE
Some solutions for n=5 k=4
..4....1....4....2....1....1....2....0....1....3....1....3....0....0....1....0
..3....2....4....0....3....3....1....0....1....4....2....1....0....2....3....0
..0....4....2....3....4....0....1....4....1....3....1....4....4....1....1....3
..3....1....2....4....0....0....0....3....0....1....4....2....3....3....1....1
..2....2....1....1....2....3....1....3....1....0....4....1....0....3....4....1
..1....0....1....3....3....4....0....1....0....2....0....4....2....4....1....2
..4....1....0....0....0....4....2....4....2....4....3....0....4....2....4....0
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 27 2014
STATUS
approved