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A052276 Nonnegative numbers of the form n^3 (+/-) 3, n >= 0.

%I A052276 #28 Jun 27 2025 12:18:05
%S A052276 3,4,5,11,24,30,61,67,122,128,213,219,340,346,509,515,726,732,997,
%T A052276 1003,1328,1334,1725,1731,2194,2200,2741,2747,3372,3378,4093,4099,
%U A052276 4910,4916,5829,5835,6856,6862,7997,8003,9258,9264,10645,10651
%N A052276 Nonnegative numbers of the form n^3 (+/-) 3, n >= 0.
%C A052276 It is conjectured that A003325 and A052276 (the current sequence) have infinitely many numbers in common, although only one example (128) is known.
%C A052276 The next such example must be larger than 2*10^12. - _M. F. Hasler_, Jan 10 2021
%H A052276 T. D. Noe, <a href="/A052276/b052276.txt">Table of n, a(n) for n = 1..1000</a>
%H A052276 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3,-3,3,1,-1).
%F A052276 a(n) = a(n-1)+3*a(n-2)-3*a(n-3)-3*a(n-4)+3*a(n-5)+a(n-6)-a(n-7) for n>8. - _Colin Barker_, Jul 09 2015
%F A052276 G.f.: x*(5*x^7-8*x^6-9*x^5+19*x^4+3*x^3-8*x^2+x+3) / ((x-1)^4*(x+1)^3). - _Colin Barker_, Jul 09 2015
%F A052276 a(n) = ((2*n+1)*(n^2+n+1) - (-1)^n*(3*n^2+3*n-47))/16 for n >= 2. - _Robert Israel_, Jul 09 2015
%F A052276 a(n) = ceiling(n/2)^3 + 3*(-1)^n for all n > 1. - _M. F. Hasler_, Jan 10 2021
%p A052276 3,4,op(map(n -> (n^3-3,n^3+3), [$2..100])); # _Robert Israel_, Jul 09 2015
%o A052276 (PARI) Vec(x*(5*x^7-8*x^6-9*x^5+19*x^4+3*x^3-8*x^2+x+3)/((x-1)^4*(x+1)^3) + O(x^100)) \\ _Colin Barker_, Jul 09 2015
%o A052276 (PARI) apply( {A052276(n)=(n\/2)^3+3*(-1)^n+(n==1)*5}, [1..99]) \\ _M. F. Hasler_, Jan 10 2021
%o A052276 (Python)
%o A052276 def A052276(n): return (n+1>>1)**3+(-3 if n&1 else 3) if n>1 else 3 # _Chai Wah Wu_, Jun 27 2025
%K A052276 nonn,easy
%O A052276 1,1
%A A052276 _N. J. A. Sloane_, Feb 05 2000