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A270851 Number of 2X2X2 triangular 0..n arrays with some element plus some adjacent element totalling n+1, n or n-1 exactly once. 1

%I #4 Mar 24 2016 08:38:25

%S 0,0,6,24,66,120,198,288,402,528,678,840,1026,1224,1446,1680,1938,

%T 2208,2502,2808,3138,3480,3846,4224,4626,5040,5478,5928,6402,6888,

%U 7398,7920,8466,9024,9606,10200,10818,11448,12102,12768,13458,14160,14886,15624

%N Number of 2X2X2 triangular 0..n arrays with some element plus some adjacent element totalling n+1, n or n-1 exactly once.

%C Row 2 of A270850.

%H R. H. Hardin, <a href="/A270851/b270851.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4) for n>5

%F Empirical for n mod 2 = 0: a(n) = 9*n^2 - 42*n + 48 for n>1

%F Empirical for n mod 2 = 1: a(n) = 9*n^2 - 42*n + 51 for n>1

%e Some solutions for n=4

%e ...2....1....0....1....0....4....3....2....2....2....0....4....4....2....3....2

%e ..0.4..2.0..1.2..0.2..2.4..2.0..4.2..4.3..2.0..0.2..2.2..2.2..0.2..0.1..2.4..4.2

%Y Cf. A270850.

%K nonn

%O 1,3

%A _R. H. Hardin_, Mar 24 2016

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