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%I #6 Dec 12 2014 20:51:35
%S 2,3,4,4,11,8,5,20,37,16,6,33,96,119,32,7,48,211,436,373,64,8,67,380,
%T 1269,1880,1151,128,9,88,639,2860,7109,7836,3517,256,10,113,976,5831,
%U 19896,37881,32032,10679,512,11,140,1437,10460,49037,129648,195927
%N T(n,k)=Number of length n+1 0..k arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero
%C Table starts
%C ....2.....3.......4........5.........6..........7..........8...........9
%C ....4....11......20.......33........48.........67.........88.........113
%C ....8....37......96......211.......380........639........976........1437
%C ...16...119.....436.....1269......2860.......5831......10460.......17765
%C ...32...373....1880.....7109.....19896......49037.....103556......203615
%C ...64..1151....7836....37881....129648.....380939.....938128.....2121089
%C ..128..3517...32032...195927....810964....2810751....7989940....20567199
%C ..256.10679..129572...996933...4962056...20169871...65768448...191480917
%C ..512.32293..521256..5029417..30034672..142786013..532548628..1748028901
%C .1024.97391.2091052.25262121.180893724.1004527983.4281269376.15822382297
%H R. H. Hardin, <a href="/A250167/b250167.txt">Table of n, a(n) for n = 1..263</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 5*a(n-1) -6*a(n-2)
%F k=3: a(n) = 8*a(n-1) -21*a(n-2) +22*a(n-3) -8*a(n-4)
%F k=4: [order 8]
%F Empirical for row n:
%F n=1: a(n) = n + 1
%F n=2: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4); also a quadratic polynomial plus a constant quasipolynomial with period 2
%F n=3: a(n) = 2*a(n-1) +a(n-2) -4*a(n-3) +a(n-4) +2*a(n-5) -a(n-6); also a cubic polynomial plus a linear quasipolynomial with period 2
%F n=4: [order 12; also a quartic polynomial plus a quadratic quasipolynomial with period 12]
%F n=5: [order 24; also a polynomial of degree 5 plus a cubic quasipolynomialwith period 60]
%e Some solutions for n=5 k=4
%e ..3....0....3....4....0....3....4....4....2....4....4....2....0....4....3....1
%e ..2....0....4....2....0....4....1....4....4....1....3....1....1....2....1....1
%e ..4....4....0....4....4....2....2....2....4....3....4....3....1....2....3....3
%e ..0....2....0....1....2....1....3....2....1....0....3....2....3....1....0....4
%e ..1....2....4....1....3....1....3....3....3....0....0....2....0....4....3....3
%e ..1....0....3....2....0....1....2....4....0....4....0....2....0....2....3....1
%Y Column 1 is A000079
%Y Column 2 is A084171
%Y Row 2 is A212959
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 13 2014