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A197533 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,0,0 for x=0,1,2,3,4.

%I A197533 #7 Jun 02 2025 04:58:46
%S A197533 5,33,216,1419,9373,62586,423085,2879723,19671764,134643523,922592723,
%T A197533 6325665762,43386843099,297644913045,2042157812212,14012277918367,
%U A197533 96148923597911,659765081841360,4527301927394765,31066516652385893
%N A197533 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,0,0 for x=0,1,2,3,4.
%C A197533 Every 0 is next to 0 2's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 0's
%C A197533 Column 4 of A197537
%H A197533 R. H. Hardin, <a href="/A197533/b197533.txt">Table of n, a(n) for n = 1..210</a>
%F A197533 Empirical: a(n) = 8*a(n-1) +4*a(n-2) -79*a(n-3) -30*a(n-4) +99*a(n-5) +41*a(n-6) +263*a(n-7) -405*a(n-8) +899*a(n-9) +7150*a(n-10) +6933*a(n-11) +8469*a(n-12) -2881*a(n-13) -45032*a(n-14) -44677*a(n-15) -82181*a(n-16) -77611*a(n-17) -25835*a(n-18) +35284*a(n-19) +242999*a(n-20) +361557*a(n-21) +412582*a(n-22) +192680*a(n-23) -167729*a(n-24) -442796*a(n-25) -480857*a(n-26) -373624*a(n-27) -111734*a(n-28) -57452*a(n-29) -25481*a(n-30) +186675*a(n-31) -47892*a(n-32) +194240*a(n-33) +243447*a(n-34) +94789*a(n-35) +253036*a(n-36) -22990*a(n-37) -5434*a(n-38) -112176*a(n-39) -176692*a(n-40) -20055*a(n-41) -59142*a(n-42) -41241*a(n-43) +34876*a(n-44) -30663*a(n-45) +12856*a(n-46) +1495*a(n-47) +26166*a(n-48) +13268*a(n-49) +10725*a(n-50) +8787*a(n-51) -4719*a(n-52) +2299*a(n-53) -1952*a(n-54) +414*a(n-55) +118*a(n-56) -729*a(n-57) -38*a(n-58) -281*a(n-59) -97*a(n-60) -73*a(n-61) -40*a(n-62) -34*a(n-63) -24*a(n-64) -8*a(n-65) -2*a(n-66)
%e A197533 Some solutions containing all values 0 to 4 for n=5
%e A197533 ..0..3..0..0....0..3..0..0....0..3..0..0....1..0..3..0....2..1..2..1
%e A197533 ..3..0..3..1....0..0..0..0....3..0..4..0....1..0..0..3....1..0..3..0
%e A197533 ..0..4..0..1....3..0..4..0....0..4..0..3....1..0..4..0....1..0..0..0
%e A197533 ..0..0..3..2....0..3..0..0....0..0..3..0....2..3..0..3....1..0..4..0
%e A197533 ..0..3..0..1....1..2..1..1....1..1..2..1....1..0..0..0....1..0..0..0
%K A197533 nonn
%O A197533 1,1
%A A197533 _R. H. Hardin_ Oct 16 2011