A270609 - OEIS

%I #4 Mar 20 2016 11:04:33

%S 0,0,8808,171576,1728288,13177740,70129212,309511644,1134068490,

%T 3559466436,10133969880,25490692140,60750723804,131276815188,

%U 274807319832,531982013820,1009843336080,1799168710884,3165521551848

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

%C Row 4 of A270606.

%H R. H. Hardin, <a href="/A270609/b270609.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) for n>33

%F Empirical for n mod 2 = 0: a(n) = 36*n^9 - 936*n^8 + 12600*n^7 - 110928*n^6 + 693084*n^5 - 3156192*n^4 + 10401756*n^3 - 23778456*n^2 + 34012980*n - 23053764 for n>15

%F Empirical for n mod 2 = 1: a(n) = 36*n^9 - 936*n^8 + 12816*n^7 - 117516*n^6 + 783468*n^5 - 3895902*n^4 + 14328570*n^3 - 37318686*n^2 + 62032434*n - 49736268 for n>15

%e Some solutions for n=4

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

%e ....0.4......1.0......1.1......0.2......0.1......0.0......4.4......0.0

%e ...0.2.2....2.0.4....4.0.1....0.0.2....1.1.0....4.0.1....4.2.4....2.4.4

%e ..2.0.4.3..4.4.4.2..0.0.1.3..0.1.0.1..4.3.1.1..2.0.0.3..2.2.0.3..2.0.0.1

%Y Cf. A270606.

%K nonn

%O 1,3

%A _R. H. Hardin_, Mar 20 2016