A296550 - OEIS

%I #14 Jan 21 2022 14:37:57

%S 1,1,3,5,7,10,17,28,43,66,105,168,264,413,651,1030,1624,2555,4025,

%T 6349,10010,15771,24851,39173,61748,97315,153366,241722,380989,600470,

%U 946375,1491567,2350860,3705166,5839638,9203761,14505951,22862658,36033501

%N Number of n X 4 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 3 or 6 neighboring 1s.

%C Appears to be the number of tilings of a 7 X 2n rectangle with 7 X 1 heptominoes. - _M. Poyraz Torcuk_, Dec 25 2021

%H R. H. Hardin, <a href="/A296550/b296550.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 2*a(n-4) + a(n-7).

%F Empirical g.f.: x*(1 + 2*x^2 + 2*x^3 + x^5 + x^6) / (1 - x - 2*x^4 - x^7). - _Colin Barker_, Feb 23 2019

%e Some solutions for n=7:

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

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

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

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

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

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

%e   0 0 0 0    0 0 0 0    0 0 0 0    0 0 0 0    0 0 0 0

%Y Column 4 of A296554.

%K nonn

%O 1,3

%A _R. H. Hardin_, Dec 15 2017