A305219 - OEIS

%I #4 May 27 2018 17:35:10

%S 0,9,15,49,170,581,2184,7680,28315,102908,375864,1374468,5018055,

%T 18347377,67036712,245038336,895604222,3273509712,11965243920,

%U 43734676685,159858697264,584313110135,2135780659951,7806706628138

%N Number of nX4 0..1 arrays with every element unequal to 2, 3, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

%C Column 4 of A305223.

%H R. H. Hardin, <a href="/A305219/b305219.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) +4*a(n-2) +a(n-3) -12*a(n-4) -29*a(n-5) -55*a(n-6) -57*a(n-7) -86*a(n-8) +132*a(n-9) +461*a(n-10) +978*a(n-11) +2285*a(n-12) +2447*a(n-13) +2681*a(n-14) -5195*a(n-15) -13204*a(n-16) -25311*a(n-17) -29426*a(n-18) -19223*a(n-19) -23315*a(n-20) +35603*a(n-21) +106580*a(n-22) +196351*a(n-23) +134710*a(n-24) +116741*a(n-25) +111111*a(n-26) -87917*a(n-27) -128435*a(n-28) -55749*a(n-29) +147577*a(n-30) -85101*a(n-31) +212134*a(n-32) -342788*a(n-33) -1087796*a(n-34) -2189755*a(n-35) -2015867*a(n-36) -1673398*a(n-37) -4129999*a(n-38) -2797243*a(n-39) -2372528*a(n-40) -1410690*a(n-41) -1178217*a(n-42) -433973*a(n-43) +2223183*a(n-44) +1174280*a(n-45) +1907328*a(n-46) +2450317*a(n-47) +1325887*a(n-48) -315917*a(n-49) -96055*a(n-50) +139247*a(n-51) -415657*a(n-52) -185020*a(n-53) -32750*a(n-54) +235670*a(n-55) -122326*a(n-56) -160760*a(n-57) +145980*a(n-58) -12244*a(n-59) -22120*a(n-60) +6912*a(n-61) +592*a(n-62) +2864*a(n-63) -1152*a(n-64) -192*a(n-65) for n>66

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A305223.

%K nonn

%O 1,2

%A _R. H. Hardin_, May 27 2018