A253129 T(n,k)=Number of length n+2 0..k arrays with the sum of medians of adjacent triples multiplied by some arrangement of +-1 equal to zero

4, 7, 12, 10, 53, 16, 13, 152, 90, 40, 16, 345, 281, 393, 64, 19, 676, 673, 2058, 952, 144, 22, 1197, 1356, 7257, 6515, 3323, 256, 25, 1968, 2452, 19990, 28428, 32166, 9205, 544, 28, 3057, 4083, 46945, 92041, 184145, 119317, 29445, 1024, 31, 4540, 6409, 98124

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

Row 1 is A016777

Sequence in context: A072732 A270684 A083487 * A249918 A340244 A158937

Adjacent sequences: A253126 A253127 A253128 * A253130 A253131 A253132

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 27 2014

Status

approved