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
Offset: 1
Keywords
Examples
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
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Programs
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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 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
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
Comments