[?] Find a closed formula given a sequence?

Questions
1

Hello! I am having trouble making closed formulas for two given sequences, and I would love if I got some help!
The two problems are to find the closed formulas for the two sequences:

{3,7,14,24,37,53,72,...}

and

{1,2,21,76,185,366,637,1016,1521,2170,....}

Thank you!

2

Hi,

what about:

FindSequenceFunction[{3, 7, 14, 24, 37, 53, 72}, n]
(*1/2 (4 - n + 3 n^2)*)

and

FindSequenceFunction[{1, 2, 21, 76, 185, 366, 637, 1016, 1521, 2170},n]
(*7 n - 9 n^2 + 3 n^3*)

Cheers,

Marco

3

Another way:

datax = Range[7];
datay = {3, 7, 14, 24, 37, 53, 72};
data = Transpose[{datax, datay}];
FindFormula[data, n, 1] // Rationalize
(* 2 - n/2 + (3 n^2)/2 *)

datax = Range[10];
datay = {1, 2, 21, 76, 185, 366, 637, 1016, 1521, 2170};
data = Transpose[{datax, datay}];
FindFormula[data, n, 1] // Rationalize
(* 7 n - 9 n^2 + 3 n^3 *)

Regards,MI