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Question Number 207979 by Tawa11 last updated on 01/Jun/24

generate nth term for the sequence: 1, 1, 1, 2, 3, 5, 9, 18, 35, 75

Commented by Frix last updated on 02/Jun/24

Look there: oeis.org/A000602

Commented by Frix last updated on 02/Jun/24

$$\mathrm{We}\mathrm{could}\mathrm{find}\mathrm{a}\mathrm{polynomial}\mathrm{of}{9}^{\mathrm{th}}\mathrm{degree}$$$$\mathrm{but}\mathrm{it}{\mathrm{doesn}}^{\prime }\mathrm{t}\mathrm{fit}\mathrm{the}\mathrm{sequence}\mathrm{in}\mathrm{the}\mathrm{link}\mathrm{I}$$$$\mathrm{posted}.$$

Commented by Tawa11 last updated on 03/Jun/24

$$\mathrm{Thanks}\mathrm{sir}.\mathrm{I}\mathrm{appreciate}$$

Answered by Berbere last updated on 02/Jun/24

$$noteUnique;$$$$moreGeneraly$$$$p\left(a_1\right)=x_1;.....p\left(a_n\right)=x_n$$$$p\left(x\right)=\underset{i=1}{\sum ^n}p\left(a_i\right).\underset{j=1;j\ne i}{\prod ^n}\frac{(x-a_j)}{(a_i-a_j)}LagrangePolynomial$$$$p\left(1\right)=1;p\left(2\right)=1;p\left(3\right)=1.......$$$$$$

Commented by Tawa11 last updated on 03/Jun/24

$$\mathrm{Thanks}\mathrm{sir}.\mathrm{I}\mathrm{appreciate}$$

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