求数列 {a(n)}={ 1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,… } 的通项公式

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求: 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, ...通项公式。

1个1, 3个2, 6个3, 10个4, 15个5, 21个6, ......，n(n+1)/2个 n。

luyuanhong

王守恩

luyuanhong 发表于 2024-7-14 12:36

谢谢陆老师！自己无端的搞了一个。请陆老师指点。 谢谢！
   
\(a(n)=\bigg\lfloor\sqrt[3]{6n}+\frac{n+1}{(3n+\pi)\sqrt[3]{6n}}\bigg\rfloor\)

OEIS——A360010——可没有通项公式的。

王守恩

luyuanhong 发表于 2024-7-14 12:36

陆老师！一直想问，一直不敢问，憋不住,还是问。

求: 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, ...通项公式。

1个1, 2个2, 4个3, 7个4, 11个5, 16个6, ......，n(n-1)/2+1个 n。

luyuanhong

王守恩

0, 0, 1, 2, 4, 6, 9, 12, 16, 20, 25, 30, 36, 42, 49, 56, 64, 72, 81, 90, 100, 110, 121, 132, 144, 156, 169, 182, 196, 210, 225, 240, 256, 272, 289, 306, 324, 342, 361, 380, 400, 420, 441, 462, 484, 506,
529, 552, 576, 600, 625, 650, 676, 702, 729, 756, 784, 812, 841, 870, 900, 930, 961, 992, 1024, 1056, 1089, 1122, 1156, 1190, 1225, 1260, 1296, 1332, 1369, 1406, 1444, 1482, 1521, 1560, ......

\(a(n)=\big\lfloor\frac{n}{\sqrt[n]{e^4} - 1}\big\rfloor\)

王守恩

求通项公式。

{0, 1, 0, 1, 2, 1, 2, 1, 2, 4, 2, 4, 2, 4, 2, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12,
16, 12, 16, 12, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 25, 20, 25, 20, 25, 20, 25, 20, 25, 20, 25, 20, 25, 20, 25, 20, 25, 20, 25, 30, 25, 30, 25,
30, 25, 30, 25, 30, 25, 30, 25, 30, 25, 30, 25, 30, 25, 30, 25, 30, 36, 30, 36, 30, 36, 30, 36, 30, 36, 30, 36, 30, 36, 30, 36, 30, 36, 30, 36, 30, 36, 30, 36, 42, 36, 42, 36, 42,
36, 42, 36, 42, 36, 42, 36, 42, 36, 42, 36, 42, 36, 42, 36, 42, 36, 42, 36, 42, 49, 42, 49, 42, 49, 42, 49, 42, 49, 42, 49, 42, 49, 42, 49, 42, 49, 42, 49, 42, 49, 42, 49, 42, 49,
42, 49, 56, 49, 56, 49, 56, 49, 56, 49, 56, 49, 56, 49, 56, 49, 56, 49, 56, 49, 56, 49, 56, 49, 56, 49, 56, 49, 56, 49, 56, 64, 56, 64, 56, 64, 56, 64, 56, 64, 56, 64, 56, 64,......,

0有2个。1有4个。2有6个。4有8个。6有10个。9有12个。12有14个。16有16个。20有18个。25有20个。30有22个。36有24个。42有26个。49有28个。56有30个。64有32个。

1. Table[Round[n^2/4] - Round[(n + Sqrt[n])/2] Round[(n - Sqrt[n])/2], {n, 260}]

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