A298926 - OEIS

%I #6 Sep 04 2022 13:20:04

%S 0,2,4,11,23,72,201,597,1717,5183,15479,46260,138928,417427,1255369,

%T 3777004,11372190,34247960,103164581,310821235,936579808,2822417917,

%U 8506019597,25636254701,77267796877,232891865309,701970354408

%N Number of n X 4 0..1 arrays with every element equal to 2, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Column 4 of A298930.

%H R. H. Hardin, <a href="/A298926/b298926.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) -10*a(n-2) +7*a(n-3) -23*a(n-4) +31*a(n-5) -15*a(n-6) +104*a(n-7) -147*a(n-8) +182*a(n-9) -366*a(n-10) +376*a(n-11) -685*a(n-12) +689*a(n-13) -613*a(n-14) +1143*a(n-15) -710*a(n-16) -129*a(n-17) -82*a(n-18) -584*a(n-19) +5620*a(n-20) -1356*a(n-21) +6298*a(n-22) -15575*a(n-23) +6568*a(n-24) -15985*a(n-25) +6661*a(n-26) -23488*a(n-27) +19556*a(n-28) +16109*a(n-29) +18333*a(n-30) +8059*a(n-31) -12197*a(n-32) +16533*a(n-33) -27875*a(n-34) -8576*a(n-35) -28209*a(n-36) +16299*a(n-37) +26487*a(n-38) +4040*a(n-39) -22226*a(n-40) +1134*a(n-41) -9128*a(n-42) -7294*a(n-43) +16692*a(n-44) +6504*a(n-45) +1137*a(n-46) -5253*a(n-47) +2127*a(n-48) -324*a(n-49) +1885*a(n-50) -1689*a(n-51) -59*a(n-52) -235*a(n-53) +346*a(n-54) -86*a(n-55) +12*a(n-56) -46*a(n-57) +24*a(n-58) +8*a(n-59) -4*a(n-60) for n>61.

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A298930.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 29 2018