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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

%I

%S 4,7,12,10,53,16,13,152,90,40,16,345,281,393,64,19,676,673,2058,952,

%T 144,22,1197,1356,7257,6515,3323,256,25,1968,2452,19990,28428,32166,

%U 9205,544,28,3057,4083,46945,92041,184145,119317,29445,1024,31,4540,6409,98124

%N 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

%C Table starts

%C ....4......7......10........13.........16.........19..........22...........25

%C ...12.....53.....152.......345........676.......1197........1968.........3057

%C ...16.....90.....281.......673.......1356.......2452........4083.........6409

%C ...40....393....2058......7257......19990......46945.......98124.......187593

%C ...64....952....6515.....28428......92041.....246003......570578......1191085

%C ..144...3323...32166....184145.....764836....2521335.....7036012.....17264207

%C ..256...9205..119317....866944....4373134...16987236....54817908....153203700

%C ..544..29445..517390...4737473...29088446..134079743...503679532...1613885479

%C .1024..85717.2015982..23297196..172527610..932611547..4023378619..14596031060

%C .2112.264455.8326770.120376601.1072084446.6789960255.33615995160.137794713707

%H R. H. Hardin, <a href="/A253129/b253129.txt">Table of n, a(n) for n = 1..221</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1) +2*a(n-2) -4*a(n-3)

%F k=2: [order 16]

%F k=3: [order 63] for n>64

%F Empirical for row n:

%F n=1: a(n) = 3*n + 1

%F n=2: a(n) = (1/3)*n^4 + (8/3)*n^3 + (14/3)*n^2 + (10/3)*n + 1

%F 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)

%F n=4: [order 15]

%F Empirical quasipolynomials for row n:

%F n=3: polynomial of degree 4 plus a quasipolynomial of degree 1 with period 2

%F n=4: polynomial of degree 6 plus a quasipolynomial of degree 3 with period 3

%e Some solutions for n=5 k=4

%e ..4....1....4....2....1....1....2....0....1....3....1....3....0....0....1....0

%e ..3....2....4....0....3....3....1....0....1....4....2....1....0....2....3....0

%e ..0....4....2....3....4....0....1....4....1....3....1....4....4....1....1....3

%e ..3....1....2....4....0....0....0....3....0....1....4....2....3....3....1....1

%e ..2....2....1....1....2....3....1....3....1....0....4....1....0....3....4....1

%e ..1....0....1....3....3....4....0....1....0....2....0....4....2....4....1....2

%e ..4....1....0....0....0....4....2....4....2....4....3....0....4....2....4....0

%Y Row 1 is A016777

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 27 2014

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Last modified August 4 18:15 EDT 2021. Contains 346455 sequences. (Running on oeis4.)