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%I #37 May 03 2021 09:52:05
%S 0,1,8,26,56,99,160,244,352,485,648,846,1080,1351,1664,2024,2432,2889,
%T 3400,3970,4600,5291,6048,6876,7776,8749,9800,10934,12152,13455,14848,
%U 16336,17920,19601,21384,23274,25272,27379,29600,31940,34400,36981,39688,42526
%N a(n) = n^3 - a(n-2) for n >= 2 and a(0)=0, a(1)=1.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-7,8,-7,4,-1).
%F G.f.: (x+4*x^2+x^3)/((-1+x)^4*(1+x^2)). - _David Scambler_, Aug 06 2012
%F a(n) = (n*(n^2-3)-(1-(-1)^n)*i^(n+1))/2, where i=sqrt(-1). - _Bruno Berselli_, Aug 07 2012
%t RecurrenceTable[{a[0] == 0, a[1] == 1, a[n] == n^3 - a[n - 2]}, a[n], {n, 0, 43}] (* _Bruno Berselli_, Aug 07 2012 *)
%o (Python)
%o prpr = 0
%o prev = 1
%o for n in range(2,77):
%o print(prpr, end=',')
%o curr = n*n*n - prpr
%o prpr = prev
%o prev = curr
%Y Cf. A000217 (n^2 - a(n-1)).
%Y Cf. A125577 (n^2 - a(n-1) with a(0)=1).
%Y Cf. A011934 (n^3 - a(n-1)).
%Y Cf. A153026 (n^3 - a(n-1) with a(1)=0).
%Y Cf. A194274 (n^2 - a(n-2)).
%Y Cf. A187093 (n^2 - a(n-2) with a(0)=a(1)=1, a(-1)=0).
%Y Cf. A107386 ((n-2)^2 - a(n-1) with a(0)=0, a(1)=a(2)=1, a(3)=2).
%Y Cf. A206481 ((n-1)^3 - a(n-2)).
%K nonn,easy
%O 0,3
%A _Alex Ratushnyak_, Aug 03 2012
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