A300085 - OEIS

%I #6 Feb 25 2018 06:17:19

%S 5,8,4,25,50,98,359,766,1932,5677,12860,34902,92923,224468,609898,

%T 1569799,3969016,10617506,27213371,70541934,186417464,481204483,

%U 1261639106,3316784004,8641317351,22770348996,59873020940,157234586213

%N Number of nX4 0..1 arrays with every element equal to 0, 1, 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Column 4 of A300089.

%H R. H. Hardin, <a href="/A300085/b300085.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) +a(n-2) +23*a(n-3) -77*a(n-4) +5*a(n-5) -303*a(n-6) +735*a(n-7) -169*a(n-8) +2494*a(n-9) -3571*a(n-10) +1775*a(n-11) -10599*a(n-12) +9687*a(n-13) -8801*a(n-14) +23592*a(n-15) -19900*a(n-16) +18698*a(n-17) -34363*a(n-18) +29869*a(n-19) -21710*a(n-20) +36339*a(n-21) -31007*a(n-22) +16036*a(n-23) -26673*a(n-24) +26280*a(n-25) -4804*a(n-26) +15200*a(n-27) -19964*a(n-28) -4002*a(n-29) -9745*a(n-30) +12193*a(n-31) +4104*a(n-32) +5170*a(n-33) -7137*a(n-34) -2131*a(n-35) -834*a(n-36) +4727*a(n-37) +2072*a(n-38) -544*a(n-39) -2800*a(n-40) -1833*a(n-41) +287*a(n-42) +1272*a(n-43) +1184*a(n-44) -38*a(n-45) -361*a(n-46) -569*a(n-47) -23*a(n-48) +69*a(n-49) +172*a(n-50) +27*a(n-51) -23*a(n-52) -34*a(n-53) -10*a(n-54) +5*a(n-55) +7*a(n-56) +a(n-57) -a(n-59) for n>61

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A300089.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 24 2018