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%I #4 Dec 27 2014 09:36:29
%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