A297947 - OEIS

%I #4 Jan 09 2018 07:33:58

%S 2,52,219,948,4258,19561,88441,402245,1831311,8330961,37894374,

%T 172425675,784486903,3569125339,16238621755,73881624965,336140947838,

%U 1529351967657,6958148321122,31657725977397,144034249072846,655317671930897

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

%C Column 4 of A297951.

%H R. H. Hardin, <a href="/A297947/b297947.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) -21*a(n-2) +54*a(n-3) -200*a(n-4) +342*a(n-5) -446*a(n-6) +1223*a(n-7) -807*a(n-8) -1330*a(n-9) +1563*a(n-10) -10480*a(n-11) +24684*a(n-12) -29302*a(n-13) +57265*a(n-14) -78482*a(n-15) +46625*a(n-16) -62084*a(n-17) -8460*a(n-18) +272147*a(n-19) -420190*a(n-20) +976617*a(n-21) -1705350*a(n-22) +2135163*a(n-23) -3355799*a(n-24) +3688408*a(n-25) -3510994*a(n-26) +4120995*a(n-27) -1724506*a(n-28) +485319*a(n-29) -1048327*a(n-30) -4310085*a(n-31) +3179761*a(n-32) +98309*a(n-33) +6473166*a(n-34) -1966316*a(n-35) -3346076*a(n-36) -5649149*a(n-37) +1912190*a(n-38) +2272624*a(n-39) +7702451*a(n-40) -2469037*a(n-41) -1669127*a(n-42) -3107416*a(n-43) -2412890*a(n-44) +2281904*a(n-45) +646517*a(n-46) +1539380*a(n-47) -70041*a(n-48) -487558*a(n-49) -432384*a(n-50) -170359*a(n-51) -114913*a(n-52) +134192*a(n-53) +56535*a(n-54) +31739*a(n-55) +31645*a(n-56) +1402*a(n-57) -8896*a(n-58) -2156*a(n-59) -64*a(n-60) +130*a(n-61) +816*a(n-62) +254*a(n-63) -94*a(n-64) -72*a(n-65) -16*a(n-66) for n>69

%e Some solutions for n=7

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

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

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

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

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

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

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

%Y Cf. A297951.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 09 2018