P1st Q1st even
[1,] 0 0 1
[2,] 4 5 6
[3,] 26 27 13
[4,] 84 83 23
[5,] 203 197 35
[6,] 413 398 50
[7,] 751 722 67
[8,] 1259 1210 87
[9,] 1986 1910 109
[10,] 2986 2875 134

完全追尾型多項式が完成しました

宝の個数を２で固定します

P1st =｛12n^4+28n^3-42n^2-52n-3(-1)^n+51｝/48

Q1st =｛12n^4+20n^3-18n^2-20n-3(-1)^n+3｝/48

even =(10n^2+8n+(-1)^n-9)/8

■Wolframに入力すると既約分数表示になるので御注意

P1st／Q1st

=｛8(n-1)｛(n-2)n-6｝/｛2n(n+2)(6n^2-2n-5)-3(-1)^n+3｝｝+1