I'm trying to analyze the following sequence of numbers:
$$a_1 = 2 \quad \text{ s.t } \quad a_n = 4\sum_{i=1}^{n}a_i $$ I wrote the following code for creating a Recurrence Table for this sequence of numbers:
rt = RecurrenceTable[{a[n + 1] == 4 Sum[a[n], {1, n}], a[1] == 2}, a, {n, 1, 10}]
But, I'm facing the following issue, when I try to evaluate the actual numerical value, I'm getting the following format as output:
$rt[[2]] = 4 \times \sum_{1}^{1}2$
Even when I run
N[rt[[2]]
The output is
4. NSum[2, {1, 1}]
The ouput for the FullForm is:
\!\(
TagBox[
StyleBox[
RowBox[{"Times", "[",
RowBox[{"4", ",",
RowBox[{"Sum", "[",
RowBox[{"2", ",",
RowBox[{"List", "[",
RowBox[{"1", ",", "1"}], "]"}]}], "]"}]}], "]"}],
ShowSpecialCharacters->False,
ShowStringCharacters->True,
NumberMarks->True],
FullForm]\)
Any tips on how to get the numerical values? Is the error in the actual function for the definition of the Recurrence Table?