蔡家雄 发表于 2023-12-28 13:49
f(n)=1, 4, 15, 56, 209, 780, 2911, 10864, 40545, 151316, 564719, 2107560, 7865521, 29354524, 1095525 ...
有道理。b(n)在OEIS搜索不到。f(n)在OEIS是可以搜索的。
\(b(n)=\lfloor\frac{ (2 + \sqrt{3})^{2 n}}{2 \sqrt{3}}\rfloor\)
b(n)=0, 4, 56, 780, 10864, 151316, 2107560, 29354524, 408855776, 5694626340,
79315912984, 1104728155436, 15386878263120, 214311567528244, ......
\(f(n)=\lfloor\frac{ (2 + \sqrt{3})^{n}}{2 \sqrt{3}}\rfloor\) 我们的通项公式简单些。
f(n)=1, 4, 15, 56, 209, 780, 2911, 10864, 40545, 151316, 564719, 2107560, 7865521, 29354524, 109552575, 408855776, 1525870529, 5694626340, 21252634831, 79315912984, 296011017105, 1104728155436, 4122901604639, 15386878263120, 57424611447841, 214311567528244, ... |