0, 1, 4, 9, 16, 25, 36, ... =
A000290(n)
0, 5, 19, 40, 69, 107, 152, ... = a(n)
0, 1, 5, 11, 18, 28, 40, ... =
A240438(n+1)
1, 9, 25, 49, 81, 121, 169, ... =
A016754(n)
0, 2, 7, 13, 21, 32, 44, ... =
A262523(n)
3, 13, 32, 59, 93, 136, 187, ... = e(n+1).
The five-step recurrence in FORMULA is valuable for the six sequences.
Consider a(n) extended from right to left with their first two differences:
..., 59, 32, 13, 3, 0, 5, 19, 40, 69, ...
..., -27, -19, -10, -3, 5, 14, 21, 29, 38, ...
..., 8, 9, 7, 8, 9, 7, 8, 9, 7, ... .
From 0,the first row is
1) from right to left: e(n)
2) from left to right: a(n).
a(n) and e(n) are companions.
The third row is of period 3.
The last digit of a(n) is of period 15; the same is true of e(n).
