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A270853 Number of 4X4X4 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 08:41:02

%S 0,0,252,6822,108348,1144464,8559378,49511370,225803628,868915644,

%T 2866094766,8402366160,22207133946,53934812124,121777854570,

%U 258248878044,519141258054,994719606876,1830153826026,3242675095548,5566018125510

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

%C Row 4 of A270850.

%H R. H. Hardin, <a href="/A270853/b270853.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) = 54*n^9 - 2304*n^8 + 48114*n^7 - 640560*n^6 + 5967942*n^5 - 40260606*n^4 + 196350792*n^3 - 666434964*n^2 + 1425184728*n - 1458389412 for n>15

%F Empirical for n mod 2 = 1: a(n) = 54*n^9 - 2304*n^8 + 48141*n^7 - 641856*n^6 + 5994894*n^5 - 40583919*n^4 + 198797448*n^3 - 678190998*n^2 + 1458498405*n - 1501345395 for n>15

%e Some solutions for n=4

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

%e ....1.0......4.4......0.1......4.4......3.4......0.2......2.0......0.0

%e ...0.1.1....2.4.4....2.0.1....3.4.2....3.3.4....0.0.0....0.0.0....0.1.2

%e ..0.2.0.1..3.4.4.4..0.1.1.1..4.3.4.3..3.4.3.3..2.0.1.0..0.0.1.0..0.0.0.0

%Y Cf. A270850.

%K nonn

%O 1,3

%A _R. H. Hardin_, Mar 24 2016

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