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A200463
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Number of 0..2 arrays x(0..n-1) of n elements with each no smaller than the sum of its four previous neighbors modulo 3.
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1
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3, 6, 12, 24, 48, 98, 199, 400, 800, 1597, 3188, 6360, 12679, 25273, 50376, 100400, 200077, 398698, 794502, 1583212, 3154828, 6286514, 12526942, 24961994, 49740765, 99116372, 197505241, 393560803, 784232662, 1562708632, 3113946596, 6205036280
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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a(n) - 3*a(n + 1) + 3*a(n + 2) - a(n + 3) + 2*a(n + 4) - 2*a(n + 5) - 4*a(n + 6) + 7*a(n + 7) - 2*a(n + 9) + 2*a(n + 10) - 10*a(n + 11) + 11*a(n + 12) + 3*a(n + 13) - 9*a(n + 14) + 7*a(n + 15) - 17*a(n + 16) + 22*a(n + 17) - 20*a(n + 18) + 24*a(n + 19) - 24*a(n + 20) + 13*a(n + 21) - 27*a(n + 22) + 36*a(n + 23) - 13*a(n + 24) - a(n + 25) - 11*a(n + 26) - 14*a(n + 27) + 42*a(n + 28) - 17*a(n + 29) + 9*a(n + 30) - 36*a(n + 31) + 17*a(n + 32) + 28*a(n + 33) - 19*a(n + 34) - 4*a(n + 35) + 22*a(n + 36) - 47*a(n + 37) + 82*a(n + 38) - 113*a(n + 39) + 135*a(n + 40) - 111*a(n + 41) + 45*a(n + 42) - a(n + 43) - 6*a(n + 44) + 43*a(n + 45) - 47*a(n + 46) + 17*a(n + 47) - 34*a(n + 48) + 42*a(n + 50) - 18*a(n + 51) + 10*a(n + 52) - 25*a(n + 53) + 45*a(n + 54) - 30*a(n + 55) - 18*a(n + 56) + 22*a(n + 57) - 20*a(n + 58) + 5*a(n + 59) + 27*a(n + 60) - 20*a(n + 61) + 5*a(n + 62) - 8*a(n + 63) + 23*a(n + 64) - 31*a(n + 65) + 14*a(n + 66) + 6*a(n + 67) - 24*a(n + 68) + 20*a(n + 69) + 5*a(n + 71) - 9*a(n + 72) + 3*a(n + 73) - 4*a(n + 74) - 6*a(n + 75) + 12*a(n + 76) - 4*a(n + 77) + 2*a(n + 79) - 3*a(n + 80) + a(n + 81) = 0. - Robert Israel, Dec 11 2023
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EXAMPLE
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Some solutions for n=6
..1....0....1....1....0....1....0....0....0....0....2....1....0....1....0....0
..2....0....2....2....0....2....0....0....1....2....2....2....0....2....2....0
..0....0....0....2....0....1....1....1....2....2....2....1....0....1....2....0
..0....0....0....2....2....2....1....2....1....2....0....1....0....2....2....1
..0....0....2....2....2....1....2....0....2....0....2....2....1....1....1....2
..2....0....2....2....1....0....2....2....1....2....0....2....2....2....1....2
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MAPLE
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Configs:= [seq(convert(81+i, base, 3)[1..4], i=0..80)]:
Compatible:= proc(i, j)
if not Configs[i][2..4]=Configs[j][1..3] then return 0 fi;
if convert(Configs[i], `+`) mod 3 <= Configs[j][4]
then 1 else 0
fi
end proc:
T:= Matrix(81, 81, Compatible):
initconfigs:= select(t -> t[1] <= t[2] and t[1]+t[2] mod 3 <= t[3] and t[1]+t[2]+t[3] mod 3 <= t[4], Configs):
u0:= Vector(81, i -> `if`(member(Configs[i], initconfigs), 1, 0)):
e:= Vector(81, 1):
3, 6, 12, seq(u0^%T . T^i . e, i=0..30); # Robert Israel, Dec 11 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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