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A250320 T(n,k)=Number of length n+2 0..k arrays with the sum of second differences squared multiplied by some arrangement of +-1 equal to zero.

%I A250320 #8 Jul 23 2025 12:17:55
%S A250320 2,5,8,8,25,8,13,60,41,24,18,117,104,161,42,25,200,233,652,487,104,32,
%T A250320 321,436,1773,2432,1689,212,41,480,745,3916,8767,12820,5849,464,50,
%U A250320 681,1152,7969,24126,57833,61092,19981,950,61,940,1733,14452,57305,197848
%N A250320 T(n,k)=Number of length n+2 0..k arrays with the sum of second differences squared multiplied by some arrangement of +-1 equal to zero.
%C A250320 Table starts
%C A250320 ....2......5.......8.......13........18.........25.........32........41
%C A250320 ....8.....25......60......117.......200........321........480.......681
%C A250320 ....8.....41.....104......233.......436........745.......1152......1733
%C A250320 ...24....161.....652.....1773......3916.......7969......14452.....24293
%C A250320 ...42....487....2432.....8767.....24126......57305.....119004....228401
%C A250320 ..104...1689...12820....57833....197848.....558541....1357424...2953265
%C A250320 ..212...5849...61092...363457...1559080....5237161...14866258..37065983
%C A250320 ..464..19981..300616..2317841..12424332...50020061..166783380.476368553
%C A250320 ..950..67459.1423966.14305925..95711098..461868677.1809575752
%C A250320 .1968.221953.6523576.85334033.709795516.4110975765
%H A250320 R. H. Hardin, <a href="/A250320/b250320.txt">Table of n, a(n) for n = 1..127</a>
%F A250320 Empirical for column k:
%F A250320 k=1: a(n) = 3*a(n-1) -6*a(n-3) +3*a(n-4) +3*a(n-5) -2*a(n-6)
%F A250320 Empirical for row n:
%F A250320 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 A250320 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
%e A250320 Some solutions for n=5 k=4
%e A250320 ..2....2....4....4....0....3....1....4....2....1....4....0....4....4....2....2
%e A250320 ..3....3....3....4....2....4....0....3....4....1....2....0....0....4....2....1
%e A250320 ..2....0....3....1....0....0....2....0....3....0....2....2....2....3....2....1
%e A250320 ..1....4....0....0....1....4....4....1....4....1....0....4....1....4....1....0
%e A250320 ..4....1....1....0....3....0....2....0....3....0....2....0....3....0....3....4
%e A250320 ..3....2....0....2....4....1....4....1....2....2....3....0....2....2....3....2
%e A250320 ..4....3....1....0....2....2....3....4....4....4....1....4....4....0....1....3
%Y A250320 Row 1 is A000982(n+1)
%K A250320 nonn,tabl
%O A250320 1,1
%A A250320 _R. H. Hardin_, Nov 18 2014