$n=%v$

因為一個奇數不管加\幾個偶數都還是奇數

Forward

重複組合(2)

s = 0 (slider from 0 to 46, step 1)
n = 12 (slider from 12 to 18, step 2)
A = (-14.401196206896623, 2.1003630365329444)
text2: "原題相當於將" + (LaTeX[n]) + "個相同的球分給x,y,z,u,等4個人，\\
每人可兼得或不得\\\fgcolor{yellow}{" + (LaTeX[If[s ≥ 3, "所求即" + n + "個相同的球與3個隔板的直線排列數\\\frac{" + (n + 3) + "!}{" + n + "!×3!}=" + ((n + 3)! / ((6 * n!)))]]) + "\\" + (LaTeX[If[s ≥ 4, "也可以說是H^4_" + {n} + "=C^" + {4 + n - 1} + "_" + {n} + "=" + ((n + 3)! / ((6 * n!)))]]) + "}"
q: n / 2
r: (0.5 * (n - 8))
text4: "將" + (LaTeX[n]) + "個相同的球分給四個人，\;每人得非負偶數個\\
\fgcolor{yellow}{" + (LaTeX[If[s ≥ 16, "將" + n + "個球分成2個一組，\;共" + (n / 2) + "組"]]) + "\\" + (LaTeX[If[s ≥ 17, "將" + (n / 2) + "組球分給4個人，\;每人可兼得或不得"]]) + "\\" + (LaTeX[If[s ≥ 18, "將" + (n / 2) + "組相同球與3個隔板排列"]]) + "\\" + (LaTeX[If[s ≥ 19, "\frac{" + (q + 3) + "!}{" + q + "!×3!}"]]) + "" + (LaTeX[If[s ≥ 20, "=" + ((q + 3)! / ((6 * q!)))]]) + "\\" + (LaTeX[If[s ≥ 21, "或H_" + {q} + "^4"]]) + "" + (LaTeX[If[s ≥ 22, "=C^{4+" + q + "-1}_" + {q} + ""]]) + "" + (LaTeX[If[s ≥ 23, "=" + ((q + 3)! / ((6 * q!)))]]) + "}"
b: (n - 4) / 2
text3: "將" + (LaTeX[n]) + "個相同的球分給x,y,z,u等4人,每人至少1球\\
\fgcolor{yellow}{" + (LaTeX[If[s ≥ 7, "先拿4個球分給每人一個"]]) + "\\" + (LaTeX[If[s ≥ 8, "再將剩下的" + (n - 4) + "個球，\;分給4個人，\;每人可兼得或不得"]]) + "\\" + (LaTeX[If[s ≥ 9, "所求即" + (n - 4) + "個相同的球與3個隔板的直線排列數"]]) + "\\" + (LaTeX[If[s ≥ 10, "\frac{" + (n - 1) + "!}{" + (n - 4) + "!×3!}"]]) + "" + (LaTeX[If[s ≥ 11, "=" + ((n - 1)! / ((6 * (n - 4)!)))]]) + "
\\" + (LaTeX[If[s ≥ 12, "或H_{" + (n - 4) + "}^4"]]) + "" + (LaTeX[If[s ≥ 13, "=C_{" + (n - 4) + "}^{4+" + (n - 4) + "-1}=" + ((n - 1)! / ((6 * (n - 4)!)))]]) + "
}"
text5: "將" + (LaTeX[n]) + "個球分給x,y,z,u等4人，\;每人有正偶數個\\
\fgcolor{yellow}{" + (LaTeX[If[s ≥ 26, "先分給x,y,z,u每人兩球"]]) + "\\" + (LaTeX[If[s ≥ 27, "再將剩下的" + (n - 8) + "個球，\;兩個分為一組"]]) + "\\" + (LaTeX[If[s ≥ 28, "將這" + r + "組球分給四人，\;每人可兼得或不得"]]) + "\\" + (LaTeX[If[s ≥ 29, r + "組相同的球與3個隔板排列"]]) + "\\" + (LaTeX[If[s ≥ 30, "\frac{" + (r + 3) + "!}{" + r + "!×3!}"]]) + "" + (LaTeX[If[s ≥ 31, "=" + ((r + 3)! / ((6 * r!)))]]) + "\\" + (LaTeX[If[s ≥ 32, "或H_{" + r + "}^4"]]) + "" + (LaTeX[If[s ≥ 33, "=C^{" + (4 + r - 1) + "}_{" + r + "}"]]) + "" + (LaTeX[If[s ≥ 34, "=" + ((r + 3)! / ((6 * r!)))]]) + "}"
text1: "試求：\;x+y+z+u=" + (LaTeX[n]) + "的" + (LaTeX[If[(s ≥ 1) ∧ (s ≤ 4), "(1)非負整數解；"]]) + "" + (LaTeX[If[(s ≥ 5) ∧ (s ≤ 13), "(2)正整數解；"]]) + "" + (LaTeX[If[(s ≥ 14) ∧ (s ≤ 23), "(3)非負偶數解；"]]) + "" + (LaTeX[If[(s ≥ 24) ∧ (s ≤ 34), "(4)正偶數解；"]]) + "" + (LaTeX[If[s ≥ 35, "(5)正奇數解；"]]) + ""
text6: "" + (LaTeX[If[s ≥ 35, n + "個相同球，\;分給x,y,z,u四人，\;每人有奇數個球\\"]]) + "
\fgcolor{yellow}{" + (LaTeX[If[s ≥ 38, "先分給四人每一球，\;剩下" + (n - 4) + "個球"]]) + "
\\" + (LaTeX[If[s ≥ 39, "將這" + (n - 4) + "個相同的球，\;每兩個為一組，\;分成" + ((n - 4) / 2) + "組"]]) + "\\" + (LaTeX[If[s ≥ 40, "將這" + ((n - 4) / 2) + "組球分給x,y,z,u四人，\;每人可兼得或不得"]]) + "\\" + (LaTeX[If[s ≥ 41, "即" + ((n - 4) / 2) + "組球與3個隔板的排列數"]]) + "" + (LaTeX[If[s ≥ 42, "\frac{" + (b + 3) + "!}{" + b + "!×3!}"]]) + "" + (LaTeX[If[s ≥ 43, "=" + ((b + 3)! / ((6 * b!)))]]) + "\\" + (LaTeX[If[s ≥ 44, "或H_{" + b + "}^4"]]) + "" + (LaTeX[If[s ≥ 45, "=C_{" + b + "}^{" + (b + 3) + "}"]]) + "" + (LaTeX[If[s ≥ 46, "=" + ((b + 3)! / ((6 * b!)))]]) + "
}"