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Question Number 123777 by 676597498 last updated on 28/Nov/20

Commented by MJS_new last updated on 28/Nov/20

we can find a function for any result

$$\mathrm{we}\:\mathrm{can}\:\mathrm{find}\:\mathrm{a}\:\mathrm{function}\:\mathrm{for}\:\mathrm{any}\:\mathrm{result} \\ $$

Answered by Olaf last updated on 28/Nov/20

u(n) = n^3 −1  u(2) = 7  u(3) = 26  u(4) = 63  u(5) = 124  u(6) = 215  OEIS A068601  http://oeis.org/A068601

$${u}\left({n}\right)\:=\:{n}^{\mathrm{3}} −\mathrm{1} \\ $$$${u}\left(\mathrm{2}\right)\:=\:\mathrm{7} \\ $$$${u}\left(\mathrm{3}\right)\:=\:\mathrm{26} \\ $$$${u}\left(\mathrm{4}\right)\:=\:\mathrm{63} \\ $$$${u}\left(\mathrm{5}\right)\:=\:\mathrm{124} \\ $$$${u}\left(\mathrm{6}\right)\:=\:\mathrm{215} \\ $$$$\mathrm{OEIS}\:\mathrm{A068601} \\ $$$$\mathrm{http}://\mathrm{oeis}.\mathrm{org}/\mathrm{A068601} \\ $$

Commented by MJS_new last updated on 28/Nov/20

I saw this solution too. but as you know, we  are not limited to polynomials... I′m of the  opinion, if we don′t know what we are allowed  to use, we can use what we want.  a_1 =−12  a_2 =−11  a_3 =2  a_4 =28  a_n =a_(n−4) +a_(n−3) +a_(n−2) +a_(n−1) ∀n>4  a_5 =7  a_6 =26  a_7 =63  a_8 =124  a_9 =220

$$\mathrm{I}\:\mathrm{saw}\:\mathrm{this}\:\mathrm{solution}\:\mathrm{too}.\:\mathrm{but}\:\mathrm{as}\:\mathrm{you}\:\mathrm{know},\:\mathrm{we} \\ $$$$\mathrm{are}\:\mathrm{not}\:\mathrm{limited}\:\mathrm{to}\:\mathrm{polynomials}...\:\mathrm{I}'\mathrm{m}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{opinion},\:\mathrm{if}\:\mathrm{we}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}\:\mathrm{what}\:\mathrm{we}\:\mathrm{are}\:\mathrm{allowed} \\ $$$$\mathrm{to}\:\mathrm{use},\:\mathrm{we}\:\mathrm{can}\:\mathrm{use}\:\mathrm{what}\:\mathrm{we}\:\mathrm{want}. \\ $$$${a}_{\mathrm{1}} =−\mathrm{12} \\ $$$${a}_{\mathrm{2}} =−\mathrm{11} \\ $$$${a}_{\mathrm{3}} =\mathrm{2} \\ $$$${a}_{\mathrm{4}} =\mathrm{28} \\ $$$${a}_{{n}} ={a}_{{n}−\mathrm{4}} +{a}_{{n}−\mathrm{3}} +{a}_{{n}−\mathrm{2}} +{a}_{{n}−\mathrm{1}} \forall{n}>\mathrm{4} \\ $$$${a}_{\mathrm{5}} =\mathrm{7} \\ $$$${a}_{\mathrm{6}} =\mathrm{26} \\ $$$${a}_{\mathrm{7}} =\mathrm{63} \\ $$$${a}_{\mathrm{8}} =\mathrm{124} \\ $$$${a}_{\mathrm{9}} =\mathrm{220} \\ $$

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