A298625 - OEIS

%I #4 Jan 23 2018 12:25:32

%S 0,6,26,125,1218,8617,71334,577595,4700651,38480495,314451735,

%T 2573334509,21055448310,172301801294,1410039149232,11539142575254,

%U 94432464743167,772803828389512,6324380763604258,51756745018300290,423561026286439305

%N Number of nX4 0..1 arrays with every element equal to 2, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.

%C Column 4 of A298629.

%H R. H. Hardin, <a href="/A298625/b298625.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) +32*a(n-2) -126*a(n-3) -631*a(n-4) +745*a(n-5) +5403*a(n-6) +468*a(n-7) -20718*a(n-8) -11146*a(n-9) +42419*a(n-10) +961*a(n-11) -93956*a(n-12) +20496*a(n-13) +241775*a(n-14) +62178*a(n-15) -134878*a(n-16) +248223*a(n-17) -171869*a(n-18) -835237*a(n-19) -135304*a(n-20) +777655*a(n-21) +1191282*a(n-22) -2698155*a(n-23) +243535*a(n-24) -3312164*a(n-25) +1232548*a(n-26) -4960717*a(n-27) -1263056*a(n-28) +7897251*a(n-29) +6094675*a(n-30) +5519002*a(n-31) -6891003*a(n-32) -3403376*a(n-33) +452761*a(n-34) +1113668*a(n-35) +2301629*a(n-36) -2003677*a(n-37) -244138*a(n-38) +591897*a(n-39) -347003*a(n-40) -46756*a(n-41) -141708*a(n-42) +107312*a(n-43) +78600*a(n-44) -52152*a(n-45) +14412*a(n-46) -4432*a(n-47) +408*a(n-48)

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A298629.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 23 2018