What-is-the-explicit-formula-of-this-sequence-19-151-1021-50389-

Question Number 118650 by Hassen_Timol last updated on 18/Oct/20

What is the (explicit) formula of this sequence ?

19, 151, 1021, 50389

Answered by MJS_new last updated on 18/Oct/20

zillions of possible formulas

i . e .

a_{n} = 7 960 n^{3} - 47 391 n^{2} + 86 585 n - 47 135

b_{n} = \frac{147 601 927 861 n^{3}}{694 834 860 n^{3} - 6 153 076 035 n^{2} + 13 646 831 254 n - 420 067 560}

Commented by Hassen_Timol last updated on 18/Oct/20

Thanks a lot \dots Do you know how to find ?

Commented by MJS_new last updated on 19/Oct/20

the easiest and most usual is to find a

polynome

{we}^{'} ve got 4 numbers y_{1}, y_{2}, y_{3}, y_{4}

\Rightarrow polynome of degree 3

y_{j} = {a j}^{3} + {b j}^{2} + c j + d, j = 1, 2, 3, 4

this leads to a linear system if 4 equations

in 4 unknowns a, b, c, d . solve it and {you}^{'} re

done . in this case it leads to my first solution

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