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A183644 Number of (n+1) X 2 0..4 arrays with every 2 X 2 subblock summing to 8. 1

%I #10 Mar 31 2018 14:34:29

%S 85,325,1333,5725,25405,115525,535333,2517805,11982925,57575125,

%T 278766133,1358125885,6649985245,32693825125,161264049733,

%U 797557733965,3952911584365,19625567713525,97573430562133,485654176126045

%N Number of (n+1) X 2 0..4 arrays with every 2 X 2 subblock summing to 8.

%C Column 1 of A183652.

%H R. H. Hardin, <a href="/A183644/b183644.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 15*a(n-1) - 85*a(n-2) + 225*a(n-3) - 274*a(n-4) + 120*a(n-5).

%F Conjectures from _Colin Barker_, Mar 31 2018: (Start)

%F G.f.: x*(85 - 950*x + 3683*x^2 - 5770*x^3 + 3000*x^4) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)).

%F a(n) = 2 + 2^(2+n) + 2^(3+2*n) + 2*3^(1+n) + 5^(1+n).

%F (End)

%e Some solutions for 3 X 2:

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

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

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

%Y Cf. A183652.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 06 2011

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Last modified July 17 12:34 EDT 2024. Contains 374377 sequences. (Running on oeis4.)