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A207453 T(n,k) = Number of n X k 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.

%I A207453 #8 Oct 14 2023 11:47:10
%S A207453 2,4,4,6,16,6,10,36,36,8,16,100,90,64,10,26,256,330,168,100,12,42,676,
%T A207453 1008,760,270,144,14,68,1764,3354,2560,1450,396,196,16,110,4624,10710,
%U A207453 10088,5200,2460,546,256,18,178,12100,34884,36456,23530,9216,3850,720
%N A207453 T(n,k) = Number of n X k 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.
%C A207453 Table starts
%C A207453 ..2...4...6...10....16.....26.....42......68......110......178.......288
%C A207453 ..4..16..36..100...256....676...1764....4624....12100....31684.....82944
%C A207453 ..6..36..90..330..1008...3354..10710...34884...112530...364722...1179360
%C A207453 ..8..64.168..760..2560..10088..36456..138176...509960..1910296...7096320
%C A207453 .10.100.270.1450..5200..23530..92610..396100..1610950..6754210..27799200
%C A207453 .12.144.396.2460..9216..46956.196812..932688..4086060.18819228..83939328
%C A207453 .14.196.546.3850.14896..84266.370734.1922564..8935850.44655394.212625504
%C A207453 .16.256.720.5680.22528.139984.640080.3599104.17556880.94358512.474439680
%H A207453 R. H. Hardin, <a href="/A207453/b207453.txt">Table of n, a(n) for n = 1..1573</a>
%F A207453 Empirical for column k:
%F A207453 k=1: a(n) = 2*n;
%F A207453 k=2: a(n) = 4*n^2;
%F A207453 k=3: a(n) = 12*n^2 - 6*n;
%F A207453 k=4: a(n) = 10*n^3 + 10*n^2 - 10*n;
%F A207453 k=5: a(n) = 48*n^3 - 32*n^2;
%F A207453 k=6: a(n) = 26*n^4 + 78*n^3 - 104*n^2 + 26*n;
%F A207453 k=7: a(n) = 168*n^4 - 84*n^3 - 84*n^2 + 42*n;
%F A207453 k=8: a(n) = 68*n^5 + 408*n^4 - 612*n^3 + 204*n^2;
%F A207453 k=9: a(n) = 550*n^5 - 990*n^3 + 660*n^2 - 110*n;
%F A207453 k=10: a(n) = 178*n^6 + 1780*n^5 - 2670*n^4 + 534*n^3 + 534*n^2 - 178*n;
%F A207453 k=11: a(n) = 1728*n^6 + 1440*n^5 - 6912*n^4 + 5184*n^3 - 1152*n^2;
%F A207453 k=12: a(n) = 466*n^7 + 6990*n^6 - 9320*n^5 - 2796*n^4 + 8388*n^3 - 3728*n^2 + 466*n;
%F A207453 k=13: a(n) = 5278*n^7 + 10556*n^6 - 36946*n^5 + 27144*n^4 - 3016*n^3 - 3016*n^2 + 754*n;
%F A207453 k=14: a(n) = 1220*n^8 + 25620*n^7 - 25620*n^6 - 42700*n^5 + 73200*n^4 - 36600*n^3 + 6100*n^2;
%F A207453 k=15: a(n) = 15792*n^8 + 55272*n^7 - 165816*n^6 + 98700*n^5 + 39480*n^4 - 59220*n^3 + 19740*n^2 - 1974*n.
%F A207453 Empirical for row n:
%F A207453 n=1: a(k)=a(k-1)+a(k-2);
%F A207453 n=2: a(k)=2*a(k-1)+2*a(k-2)-a(k-3);
%F A207453 n=3: a(k)=a(k-1)+7*a(k-2)+2*a(k-3)-4*a(k-4);
%F A207453 n=4: a(k)=a(k-1)+10*a(k-2)+3*a(k-3)-9*a(k-4);
%F A207453 n=5: a(k)=a(k-1)+13*a(k-2)+4*a(k-3)-16*a(k-4);
%F A207453 n=6: a(k)=a(k-1)+16*a(k-2)+5*a(k-3)-25*a(k-4);
%F A207453 n=7: a(k)=a(k-1)+19*a(k-2)+6*a(k-3)-36*a(k-4);
%F A207453 apparently for row n>2: a(k)=a(k-1)+(3*n-2)*a(k-2)+(n-1)*a(k-3)+(n-1)^2*a(k-4).
%e A207453 Some solutions for n=5, k=3
%e A207453 ..1..0..1....1..1..0....1..1..1....0..1..1....0..1..0....0..1..0....0..1..1
%e A207453 ..1..0..1....1..0..0....0..1..1....0..1..1....0..1..1....1..0..0....1..0..1
%e A207453 ..1..0..1....1..0..0....0..1..0....0..1..0....0..1..1....1..0..0....1..0..1
%e A207453 ..1..0..1....1..0..0....0..1..0....0..1..0....0..1..0....1..0..0....1..0..1
%e A207453 ..1..0..0....1..0..0....0..1..0....0..1..0....0..1..0....1..0..0....1..0..1
%Y A207453 Column 2 is A016742.
%Y A207453 Column 3 is A152746.
%Y A207453 Row 1 is A006355(n+2).
%Y A207453 Row 2 is A206981.
%K A207453 nonn,tabl
%O A207453 1,1
%A A207453 _R. H. Hardin_, Feb 17 2012