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A267958
4 times A042965.
2
0, 4, 12, 16, 20, 28, 32, 36, 44, 48, 52, 60, 64, 68, 76, 80, 84, 92, 96, 100, 108, 112, 116, 124, 128, 132, 140, 144, 148, 156, 160, 164, 172, 176, 180, 188, 192, 196, 204, 208, 212, 220, 224, 228, 236, 240, 244, 252, 256, 260, 268, 272, 276, 284, 288, 292, 300, 304
OFFSET
1,2
COMMENTS
Ordered list of differences between even squares.
FORMULA
Numbers of the form (2m)^2 - (2n)^2, sorted.
From Chai Wah Wu, Sep 01 2024: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n > 4.
G.f.: 4*x^2*(x + 1)^2/(x^4 - x^3 - x + 1). (End)
EXAMPLE
(2*0)^2 - (2*0)^2 = 0,
(2*1)^2 - (2*0)^2 = 4,
(2*2)^2 - (2*1)^2 = 12,
(2*2)^2 - (2*0)^2 = 16,
(2*3)^2 - (2*2)^2 = 20,
...
MAPLE
a := proc(n) option remember; if n = 1 then 0 elif n = 2 then 4 elif n = 3 then 12 else a(floor((1/2)*n)) + a(1+ceil((1/2)*n)) end if; end proc:
seq(a(n), n = 1..50); # Peter Bala, Aug 03 2022
PROG
(Python)
def DifferenceOfEvenSquares(maximumBound):
sequence = set([0])
for x in range(0, maximumBound+1, 4):
if x % 16 != 8:
sequence.add(x)
print(sorted(sequence))
CROSSREFS
Sequence in context: A342090 A365889 A310565 * A077770 A310566 A108269
KEYWORD
easy,nonn
AUTHOR
Matthew Burch, Jan 22 2016
STATUS
approved