A267958 4 times A042965.

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

Author

Matthew Burch, Jan 22 2016

Keywords

• easy
• nonn

Comments

Ordered list of differences between even squares.

Examples

			(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,
...
		

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Crossrefs

Cf. A008590, A042965.

Programs

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

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))

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)