Numbers with "perfect" figurate representation

[Andrew Plewe]

I propose a sequence composed of numbers which have a
"perfect" figurate representation. I think an
illustration would explain it better than words, so
here is an example:

a(1) = 77:

11 14 17 20
11 13 15 17
11 12 13 14
11 11 11 11
11 10  9  8
11  9  7  5
11  8  5  2

The representation is "perfect" because the sequences
in the columns (i.e. (8,9,10,11,12,13,14),
(5,7,9,11,13,15,17), etc.) match those centered around
the middle row. So I can start at "5" in the last
column and read leftwards (5,7,9,11) and continue with
the row starting (11,13,15,17). No numbers in the
representation can be either zero or negative. For
contrast, here is an imperfect representation:

n = 55:

11 13 15 17 19
11 12 13 14 15
11 11 11 11 11
11 10  9  8  7
11  9  7  5  3

Here the rows don't match the columns so this
representation isn't "perfect". Working by hand I've
found the following numbers have a "perfect"
representation:

25, 77, 153, 297, 533

I have a suspicion that this sequence is a.)
incomplete (i.e., there are more terms < 533 and >
533), and b.) probably covered by some other sequence
in the OEIS. Can anyone confirm if either of those are
true? 

    -Andrew Plewe-