login
Number of n X 3 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
1

%I #7 Apr 05 2018 04:09:53

%S 1,7,22,79,269,942,3401,12283,43006,156939,565249,2007662,7307653,

%T 26305407,94096702,341521831,1229036517,4413205998,15980067713,

%U 57514505187,206942767678,748087603299,2693270343273,9700931065070

%N Number of n X 3 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%C Column 3 of A302278.

%H R. H. Hardin, <a href="/A302273/b302273.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +5*a(n-2) +26*a(n-3) -66*a(n-4) -86*a(n-5) +79*a(n-6) +14*a(n-7) +13*a(n-8) -168*a(n-9) +250*a(n-10) +428*a(n-11) -232*a(n-12) -24*a(n-13) -160*a(n-14) +160*a(n-15) -256*a(n-16) -384*a(n-17) +256*a(n-18).

%e Some solutions for n=5:

%e 0 0 1 0 1 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1

%e 1 1 0 0 0 1 0 1 0 0 0 1 1 1 0 1 0 1 0 0 1

%e 1 1 1 0 1 1 0 0 1 1 1 1 0 0 0 0 1 0 1 1 1

%e 1 0 0 0 0 0 1 0 0 1 1 0 1 0 0 1 0 1 0 1 1

%e 0 1 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 1 1 0 0

%Y Cf. A302278.

%K nonn

%O 1,2

%A _R. H. Hardin_, Apr 04 2018