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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 14
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 27 2014
STATUS
approved

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Last modified May 21 02:29 EDT 2024. Contains 372720 sequences. (Running on oeis4.)