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A253129
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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
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14
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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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
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EXAMPLE
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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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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