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%I #16 Aug 04 2022 15:47:25
%S 0,4,12,16,20,28,32,36,44,48,52,60,64,68,76,80,84,92,96,100,108,112,
%T 116,124,128,132,140,144,148,156,160,164,172,176,180,188,192,196,204,
%U 208,212,220,224,228,236,240,244,252,256,260,268,272,276,284,288,292,300,304
%N 4 times A042965.
%C Ordered list of differences between even squares.
%F Numbers of the form (2m)^2 - (2n)^2, sorted.
%e (2*0)^2 - (2*0)^2 = 0,
%e (2*1)^2 - (2*0)^2 = 4,
%e (2*2)^2 - (2*1)^2 = 12,
%e (2*2)^2 - (2*0)^2 = 16,
%e (2*3)^2 - (2*2)^2 = 20,
%e ...
%p 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:
%p seq(a(n), n = 1..50); # _Peter Bala_, Aug 03 2022
%o (Python)
%o def DifferenceOfEvenSquares(maximumBound):
%o sequence = set([0])
%o for x in range(0, maximumBound+1, 4):
%o if x % 16 != 8:
%o sequence.add(x)
%o print(sorted(sequence))
%Y Cf. A008590, A042965.
%K easy,nonn
%O 1,2
%A _Matthew Burch_, Jan 22 2016
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