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
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
$$\mathrm{We}\:\mathrm{could}\:\mathrm{find}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{of}\:\mathrm{9}^{\mathrm{th}} \:\mathrm{degree} \\ $$$$\mathrm{but}\:\mathrm{it}\:\mathrm{doesn}'\mathrm{t}\:\mathrm{fit}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{in}\:\mathrm{the}\:\mathrm{link}\:\mathrm{I} \\ $$$$\mathrm{posted}. \\ $$
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
$${note}\:{Unique};\: \\ $$$${more}\:{Generaly}\: \\ $$$${p}\left({a}_{\mathrm{1}} \right)={x}_{\mathrm{1}} ;…..{p}\left({a}_{{n}} \right)={x}_{{n}} \\ $$$${p}\left({x}\right)=\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}{p}\left({a}_{{i}} \right).\underset{{j}=\mathrm{1};{j}\neq{i}} {\overset{{n}} {\prod}}\frac{\left({x}−{a}_{{j}} \right)}{\left({a}_{{i}} −{a}_{{j}} \right)}\:{Lagrange}\:{Polynomial} \\ $$$${p}\left(\mathrm{1}\right)=\mathrm{1};{p}\left(\mathrm{2}\right)=\mathrm{1};{p}\left(\mathrm{3}\right)=\mathrm{1}……. \\ $$$$ \\ $$
Commented by Tawa11 last updated on 03/Jun/24
$$\mathrm{Thanks}\:\mathrm{sir}.\:\mathrm{I}\:\mathrm{appreciate} \\ $$