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%I #4 Mar 24 2016 08:36:55
%S 0,0,0,0,0,0,0,6,0,0,0,24,30,0,0,0,66,270,252,0,0,0,120,1650,6822,
%T 2298,0,0,0,198,7344,108348,307494,28440,0,0,0,288,24954,1144464,
%U 15754872,27582438,460494,0,0,0,402,68838,8559378,469037376,5805948474,4875050400
%N T(n,k)=Number of nXnXn triangular 0..k arrays with some element plus some adjacent element totalling k+1, k or k-1 exactly once.
%C Table starts
%C .0.0......0..........0.............0................0..................0
%C .0.0......6.........24............66..............120................198
%C .0.0.....30........270..........1650.............7344..............24954
%C .0.0....252.......6822........108348..........1144464............8559378
%C .0.0...2298.....307494......15754872........469037376.........8746813158
%C .0.0..28440...27582438....5805948474.....571228600932.....29999932959600
%C .0.0.460494.4875050400.5281372355106.2104222937252028.358240737864481086
%H R. H. Hardin, <a href="/A270850/b270850.txt">Table of n, a(n) for n = 1..127</a>
%F Empirical for row n:
%F n=1: a(n) = a(n-1)
%F n=2: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4) for n>5
%F n=3: [order 10] for n>17
%F n=4: [order 18] for n>33
%F Empirical quasipolynomials for row n:
%F n=2: polynomial of degree 2 plus a quasipolynomial of degree 0 with period 2 for n>1
%F n=3: polynomial of degree 5 plus a quasipolynomial of degree 3 with period 2 for n>7
%F n=4: polynomial of degree 9 plus a quasipolynomial of degree 7 with period 2 for n>15
%e Some solutions for n=4 k=4
%e .....3........0........4........3........2........3........0........0
%e ....4.3......0.1......4.4......4.4......4.4......4.4......0.0......1.2
%e ...4.2.4....1.0.1....2.4.3....3.3.3....3.4.4....2.4.4....0.0.0....1.0.0
%e ..3.4.4.3..2.0.1.0..4.2.4.3..2.4.4.3..4.2.4.2..0.4.4.2..2.1.0.2..0.1.1.1
%K nonn,tabl
%O 1,8
%A _R. H. Hardin_, Mar 24 2016
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