|
%I #31 Aug 24 2018 12:09:20
%S 5,5,12,20,33,64,121,231,440,838,1597,3042,5796,11042,21037,40079,
%T 76357,145473,277150,528017,1005960,1916521,3651291,6956316,13252938,
%U 25249049,48103634,91645416,174599746,332641529,633737387,1207375029,2300250057,4382358586
%N Number of n X 4 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C Column 4 of A302680.
%C Empirical: The antidiagonal sums of A084534 lead to the terms of this sequence for n >= 5. - _Johannes W. Meijer_, Jun 17 2018
%H R. H. Hardin, <a href="/A302676/b302676.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) + 2*a(n-2) - a(n-4) for n > 8.
%F Empirical g.f.: x*(5 - 3*x^2 - 2*x^3 - 6*x^4 - 4*x^5 + 3*x^6 + 2*x^7) / (1 - x - 2*x^2 + x^4). - _Colin Barker_, Jun 17 2018
%F The data in the range n = 6..210 is matched by h(n) = hypergeom([-n+1, -(1/2)*n, 1/4-(1/2)*n, -(1/2)*n+1/2, -(1/2)*n+3/4], [-n, -(2/3)*n+1, -(2/3)*n+2/3, -(2/3)*n+1/3], -256/27). - _Peter Luschny_, Aug 24 2018
%e Some solutions for n=5:
%e 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 1 0 1 1 1
%e 0 1 0 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1
%e 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 1
%e 0 1 0 1 0 1 1 1 0 1 1 1 0 1 0 1 0 1 0 1
%e 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 0 0 0 1
%Y Cf. A302680, A180662 (Kn11), A084534.
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 11 2018
|
