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

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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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