A304131 - OEIS

%I #7 Oct 01 2021 17:30:41

%S 13,49,53,140,320,651,1321,2673,5293,10668,21704,43407,86685,174463,

%T 350613,704014,1416102,2846067,5718303,11503925,23146779,46553188,

%U 93651586,188449221,379193323,763054735,1535660833,3090522976,6219809542

%N Number of n X 6 0..1 arrays with every element unequal to 0, 1, 3 or 6 king-move adjacent elements, with upper left element zero.

%C Column 6 of A304133.

%H R. H. Hardin, <a href="/A304131/b304131.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 19*a(n-3) +6*a(n-4) +9*a(n-5) -153*a(n-6) -90*a(n-7) -157*a(n-8) +652*a(n-9) +559*a(n-10) +1181*a(n-11) -1404*a(n-12) -1792*a(n-13) -5054*a(n-14) +300*a(n-15) +2686*a(n-16) +13604*a(n-17) +7007*a(n-18) +884*a(n-19) -23893*a(n-20) -21475*a(n-21) -12130*a(n-22) +27170*a(n-23) +34384*a(n-24) +25529*a(n-25) -18535*a(n-26) -34229*a(n-27) -29564*a(n-28) +5242*a(n-29) +21519*a(n-30) +21219*a(n-31) +2161*a(n-32) -7919*a(n-33) -9483*a(n-34) -2452*a(n-35) +1164*a(n-36) +2492*a(n-37) +820*a(n-38) +248*a(n-39) -332*a(n-40) -96*a(n-41) -128*a(n-42) +16*a(n-43) +16*a(n-45) for n>48.

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A304133.

%K nonn

%O 1,1

%A _R. H. Hardin_, May 07 2018