A295602 - OEIS

%I #12 Nov 26 2017 14:00:11

%S 8,51,338,2305,16340,119371,892086,6775059,52046892,402986355,

%T 3136847628,24504233009,191873294724,1504755257129,11813098224356,

%U 92801573927465,729356047596030,5733901485086493,45086207743916552,354561409191514859

%N Number of n X 4 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 2, 3 or 4 1's.

%C Column 4 of A295606.

%H R. H. Hardin, <a href="/A295602/b295602.txt">Table of n, a(n) for n = 1..210</a>

%H Robert Israel, <a href="/A295602/a295602.pdf">Maple-assisted proof of formula</a>

%F Empirical: a(n) = 13*a(n-1) - 43*a(n-2) + 33*a(n-3) - 97*a(n-4) + 73*a(n-5) - 730*a(n-6) + 503*a(n-7) + 2269*a(n-8) + 2715*a(n-9) + 15348*a(n-10) + 11653*a(n-11) + 23118*a(n-12) + 14969*a(n-13) + 12525*a(n-14) - 73129*a(n-15) - 39381*a(n-16) + 23137*a(n-17) - 1963*a(n-18) + 10808*a(n-19) + 479*a(n-20) + 1751*a(n-21) + 102*a(n-22) + 5301*a(n-23) - 770*a(n-24) - 368*a(n-25) - 62*a(n-26) - 23*a(n-27).

%F Confirmed by _Robert Israel_, Nov 24 2017 (see link).

%e Some solutions for n=6:

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

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

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

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

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

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

%Y Cf. A295606.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 24 2017