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Number of 4X4X4 triangular 0..n arrays with some element plus some adjacent element totalling n+1 exactly once.
1

%I #4 Mar 18 2016 08:08:08

%S 126,5406,132474,1522068,12034134,65046258,286690914,1009836744,

%T 3156450798,8543466150,21426975306,48675627036,104954386374,

%U 210632574138,407075899314,745193641488,1325939440734,2261420632494,3772499260698

%N Number of 4X4X4 triangular 0..n arrays with some element plus some adjacent element totalling n+1 exactly once.

%C Row 4 of A270509.

%H R. H. Hardin, <a href="/A270512/b270512.txt">Table of n, a(n) for n = 1..58</a>

%F Empirical: a(n) = 2*a(n-1) +7*a(n-2) -16*a(n-3) -20*a(n-4) +56*a(n-5) +28*a(n-6) -112*a(n-7) -14*a(n-8) +140*a(n-9) -14*a(n-10) -112*a(n-11) +28*a(n-12) +56*a(n-13) -20*a(n-14) -16*a(n-15) +7*a(n-16) +2*a(n-17) -a(n-18)

%F Empirical for n mod 2 = 0: a(n) = 18*n^9 - 162*n^8 + 945*n^7 - 3462*n^6 + 8976*n^5 - 15984*n^4 + 19011*n^3 - 13479*n^2 + 4305*n

%F Empirical for n mod 2 = 1: a(n) = 18*n^9 - 162*n^8 + 972*n^7 - 3768*n^6 + 10716*n^5 - 21954*n^4 + 32355*n^3 - 32223*n^2 + 19353*n - 5181

%e Some solutions for n=3

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

%e ....0.1......0.0......1.1......1.0......1.0......0.1......0.3......2.0

%e ...0.2.0....1.1.0....0.0.0....1.2.0....1.0.3....0.2.0....1.3.2....0.2.0

%e ..3.2.1.0..2.0.1.3..0.2.2.3..3.0.0.1..0.3.3.2..0.2.0.2..2.0.0.1..2.3.0.2

%Y Cf. A270509.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 18 2016