A200463 - OEIS

A200463

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.

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

1,1

COMMENTS

Column 2 of A200469

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

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

EXAMPLE

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

MAPLE

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

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

CROSSREFS

Sequence in context: A003945 A007283 A049942 * A099844 A165929 A084717

Adjacent sequences: A200460 A200461 A200462 * A200464 A200465 A200466

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 18 2011

STATUS

approved