>>641
p(n)=((1+√(19/3))/4)^(n-1)(11√(3/19)/72+1/24)-((1-√(19/3))/4)^(n-1)(11√(3/19)/72-1/24)　（＋で表示）と
ｎ÷2の商をmとするとp(n) = Σ[i=0,i=m] n-iCi * (1/2)^(n-2i)*(1/3)^i*/6　（oで表示）
100万回のシミュレーション(赤のヒストグラム）
を重ねてみた。

https://i.imgur.com/QGpVZkd.png

前二者を少数で比較
> cbind(p(0:30),pi(0:30))
[,1] [,2]
[1,] 0.166666667 0.166666667
[2,] 0.083333333 0.083333333
[3,] 0.097222222 0.097222222
[4,] 0.076388889 0.076388889
[5,] 0.070601852 0.070601852
[6,] 0.060763889 0.060763889
[7,] 0.053915895 0.053915895
[8,] 0.047212577 0.047212577
[9,] 0.041578254 0.041578254
[10,] 0.036526653 0.036526653
[11,] 0.032122744 0.032122744
[12,] 0.028236923 0.028236923
[13,] 0.024826043 0.024826043
[14,] 0.021825329 0.021825329
[15,] 0.019188012 0.019188012
[16,] 0.016869116 0.016869116
[17,] 0.014830562 0.014830562
[18,] 0.013038320 0.013038320
[19,] 0.011462680 0.011462680
[20,] 0.010077447 0.010077447
[21,] 0.008859617 0.008859617
[22,] 0.007788957 0.007788957
[23,] 0.006847684 0.006847684
[24,] 0.006020161 0.006020161
[25,] 0.005292642 0.005292642
[26,] 0.004653041 0.004653041
[27,] 0.004090735 0.004090735
[28,] 0.003596381 0.003596381
[29,] 0.003161769 0.003161769
[30,] 0.002779678 0.002779678
[31,] 0.002443762 0.002443762

どれも正しいそう。