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A250277 T(n,k)=Number of length n+1 0..k arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.

%I A250277 #8 Jul 23 2025 12:16:34
%S A250277 2,3,4,4,11,8,5,20,27,16,6,33,52,79,32,7,48,89,240,255,64,8,67,140,
%T A250277 581,984,843,128,9,88,207,1132,2909,4412,2763,256,10,113,288,1991,
%U A250277 6732,17885,20252,8903,512,11,140,389,3156,14003,51884,107387,91808,28215,1024,12
%N A250277 T(n,k)=Number of length n+1 0..k arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.
%C A250277 Table starts
%C A250277 ....2.....3.......4........5.........6.........7..........8...........9
%C A250277 ....4....11......20.......33........48........67.........88.........113
%C A250277 ....8....27......52.......89.......140.......207........288.........389
%C A250277 ...16....79.....240......581......1132......1991.......3156........4841
%C A250277 ...32...255.....984.....2909......6732.....14003......25964.......45303
%C A250277 ...64...843....4412....17885.....51884....130335.....281552......564985
%C A250277 ..128..2763...20252...107387....381812...1154141....2908232.....6704631
%C A250277 ..256..8903...91808...636197...2783500..10172515...30143732....80256473
%C A250277 ..512.28215..406748..3664311..19762916..86975297..301550620...925066871
%C A250277 .1024.88195.1759740.20397261.135821156.715749943.2901853512.10244309701
%H A250277 R. H. Hardin, <a href="/A250277/b250277.txt">Table of n, a(n) for n = 1..181</a>
%F A250277 Empirical for column k:
%F A250277 k=1: a(n) = 2*a(n-1)
%F A250277 k=2: a(n) = 9*a(n-1) -31*a(n-2) +51*a(n-3) -40*a(n-4) +12*a(n-5) for n>6
%F A250277 k=3: [order 15] for n>18
%F A250277 Empirical for row n:
%F A250277 n=1: a(n) = n + 1
%F A250277 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
%e A250277 Some solutions for n=6 k=4
%e A250277 ..4....0....0....1....3....3....4....3....3....1....2....0....4....1....3....3
%e A250277 ..2....2....0....1....1....3....2....3....2....4....3....3....4....3....2....4
%e A250277 ..4....2....2....4....2....3....0....3....4....4....0....2....4....2....2....4
%e A250277 ..2....1....4....4....1....3....4....1....2....1....2....4....2....3....1....2
%e A250277 ..2....2....4....2....1....1....4....0....1....2....4....3....1....1....1....4
%e A250277 ..2....3....2....1....1....3....2....1....2....1....3....4....2....1....0....0
%e A250277 ..4....2....0....3....3....3....0....3....3....1....0....2....4....1....1....3
%Y A250277 Column 1 is A000079
%Y A250277 Row 2 is A212959
%K A250277 nonn,tabl
%O A250277 1,1
%A A250277 _R. H. Hardin_, Nov 16 2014