OFFSET
0,2
COMMENTS
a(n) odd terms are again A264798.
Decomposition by multiplication i.e. a(n) = b(n)*c(n) by irregular triangle:
1, 1 1,
2, 1 2,
4, 3, 2, 1, 2, 3,
6, 4, = 2, 1, * 3, 4,
9, 8, 5, 3, 2, 1, 3, 4, 5,
12, 10, 6, 3, 2, 1, 4, 5, 6,
16, 15, 12, 7, 4, 3, 2, 1, 4, 5, 6, 7,
etc. etc. etc.
Decomposition by subtraction, a(n) = d(n) - e(n):
1, 1 0,
2, 2, 0,
4, 3, 4, 3, 0, 0,
6, 4, = 6, 5, - 0, 1,
9, 8, 5, 9, 8, 7, 0, 0, 2,
12, 10, 6, 12, 11, 10, 0, 1, 4,
16, 15, 12, 7, 16, 15, 14, 13, 0, 0, 2, 6,
20, 18, 14, 8, 20, 19, 18, 17, 0, 1, 4, 9,
etc. etc. etc.
Sum of a(n) by diagonals: 1, 5, 13, 27, 48, ... . The third differences have the period 2: repeat 2, 1. See A002717.
MATHEMATICA
Table[(n + 1)^2 - k^2, {n, 15}, {k, 0, n - 1}]/4 /. _Rational -> Nothing // Flatten (* Michael De Vlieger, Mar 07 2016 *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Paul Curtz, Mar 06 2016
STATUS
approved