A304152 - OEIS

%I #6 Jul 28 2022 21:39:59

%S 0,18,42,346,1767,10182,60352,350540,2034140,11908298,69366367,

%T 404422900,2359475306,13758737304,80237613315,467966274418,

%U 2729123464612,15916133452018,92823028361780,541340687856998,3157085468272805

%N Number of n X 4 0..1 arrays with every element unequal to 2, 3, 4 or 6 king-move adjacent elements, with upper left element zero.

%C Column 4 of A304156.

%H R. H. Hardin, <a href="/A304152/b304152.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) +14*a(n-2) +23*a(n-3) -182*a(n-4) -489*a(n-5) +74*a(n-6) +2583*a(n-7) +5111*a(n-8) -1301*a(n-9) -15692*a(n-10) -25039*a(n-11) +10700*a(n-12) +55471*a(n-13) +39149*a(n-14) -100521*a(n-15) -95976*a(n-16) -11197*a(n-17) -82082*a(n-18) -337230*a(n-19) +200952*a(n-20) +1685850*a(n-21) +901791*a(n-22) +681480*a(n-23) +1540936*a(n-24) +8029675*a(n-25) -5247288*a(n-26) +4848552*a(n-27) +29842842*a(n-28) -2256018*a(n-29) -5910924*a(n-30) +29012517*a(n-31) -26670027*a(n-32) -48312547*a(n-33) +53457989*a(n-34) -33117898*a(n-35) -32241090*a(n-36) +75088419*a(n-37) -46945411*a(n-38) -41862512*a(n-39) +32206472*a(n-40) -37890914*a(n-41) -2679551*a(n-42) +42861993*a(n-43) -25134639*a(n-44) -24710989*a(n-45) +10196327*a(n-46) +5087803*a(n-47) +11182988*a(n-48) +1895982*a(n-49) -13849223*a(n-50) -116091*a(n-51) +8094101*a(n-52) +45155*a(n-53) -2178036*a(n-54) -167941*a(n-55) +2957*a(n-56) -37965*a(n-57) +45830*a(n-58) +10161*a(n-59) -1008*a(n-60) +2226*a(n-61) +413*a(n-62) -380*a(n-63) -138*a(n-64) +8*a(n-65) +8*a(n-66) for n>67.

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A304156.

%K nonn

%O 1,2

%A _R. H. Hardin_, May 07 2018