# What is the next number in the sequence: 4,9,26,105,524?

Mar 6, 2017

However, one justifiable possibility is $\textcolor{g r e e n}{1789}$
{: (color(black)("number"),color(black)("1st order"),color(black)("2nd order"),color(black)("3rd order"),color(black)("4th order")), (,color(black)("difference"),color(black)("difference"),color(black)("difference"),color(black)("difference")), (4,,,,), (,5,,,), (9,,12,,), (,17,,50,), (26,,62,,228), (,79,,278,), (105,,340,,), (,419,,,), (524,,,,) :}
If we assume that the series stabilizes with a ${4}^{t h}$ order difference of $228$,
{: (color(black)("number"),color(black)("1st order"),color(black)("2nd order"),color(black)("3rd order"),color(black)("4th order")), (,color(black)("difference"),color(black)("difference"),color(black)("difference"),color(black)("difference")), (4,,,,), (,5,,,), (9,,12,,), (,17,,50,), (26,,62,,228), (,79,,278,), (105,,340,,color(red)(228)), (,419,,color(red)(506),), (524,,color(red)(846),,), (,color(red)(1265),,,), (color(red)(1789),,,,) :}