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T(n,k)=Number of length n+2 0..k arrays with the sum of second differences multiplied by some arrangement of +-1 equal to zero
13

%I #8 Dec 12 2014 20:47:01

%S 2,5,8,8,25,14,13,60,83,32,18,117,302,297,62,25,200,761,1516,989,128,

%T 32,321,1648,5105,7126,3113,254,41,480,3125,13732,31525,30780,9611,

%U 512,50,681,5446,31173,106362,177421,127586,29257,1022,61,940,8843,63400,290909

%N T(n,k)=Number of length n+2 0..k arrays with the sum of second differences multiplied by some arrangement of +-1 equal to zero

%C Table starts

%C ....2......5.......8........13.........18.........25..........32...........41

%C ....8.....25......60.......117........200........321.........480..........681

%C ...14.....83.....302.......761.......1648.......3125........5446.........8843

%C ...32....297....1516......5105......13732......31173.......63400.......117749

%C ...62....989....7126.....31525.....106362.....290909......695890......1486139

%C ..128...3113...30780....177421.....744564....2457921.....6924692.....17094253

%C ..254...9611..127586....937817....4808120...18934449....62245658....176612641

%C ..512..29257..518052...4803653...29723864..137976845...522997696...1688068993

%C .1022..88503.2085808..24257725..180290280..980389815..4258085394..15526286669

%C .2048.266769.8367220.121800949.1085927844.6899647449.34261234132.140731044189

%H R. H. Hardin, <a href="/A250561/b250561.txt">Table of n, a(n) for n = 1..159</a>

%F Empirical for column k:

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

%F k=2: [order 10] for n>15

%F Empirical for row n:

%F n=1: 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=2: a(n) = 2*a(n-1) -a(n-2) +2*a(n-3) -4*a(n-4) +2*a(n-5) -a(n-6) +2*a(n-7) -a(n-8); also a cubic polynomial plus a linear quasipolynomial with period 3

%F n=3: [order 21; also a quartic polynomial plus a linear quasipolynomial with period 60]

%e Some solutions for n=5 k=4

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

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

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

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

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

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

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

%Y Row 1 is A000982(n+1)

%Y Row 2 is A250321

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 25 2014