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%I #21 Sep 08 2022 08:45:38
%S 0,1,9,16,24,25,33,40,48,49,57,64,72,73,81,88,96,97,105,112,120,121,
%T 129,136,144,145,153,160,168,169,177,184,192,193,201,208,216,217,225,
%U 232,240,241,249,256,264,265,273,280,288,289,297,304,312,313,321,328,336,337,345
%N Numbers n such that n^2 - n is divisible by 24.
%H Vincenzo Librandi, <a href="/A151973/b151973.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F a(n) = a(n-1)+a(n-4)-a(n-5) for n>5. G.f.: x^2*(8*x^3+7*x^2+8*x+1) / ((x-1)^2*(x+1)*(x^2+1)). - _Colin Barker_, Nov 29 2012
%F a(n) = (12*n+3*i^(n*(n-1))-2*(-1)^n-17)/2, where i=sqrt(-1). - _Bruno Berselli_, Nov 29 2012
%p A151973:=n->(12*n+3*I^(n*(n-1))-2*I^(2*n)-17)/2: seq(A151973(n), n=1..100); # _Wesley Ivan Hurt_, Jun 07 2016
%t CoefficientList[Series[x (8 x^3 + 7 x^2 + 8 x + 1) / ((x - 1)^2 (x + 1) (x^2 + 1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Jun 19 2013 *)
%o (Magma) [n: n in [0..350] | IsZero(n*(n-1) mod 24)]; // _Bruno Berselli_, Nov 29 2012
%o (PARI) is(n)=(n^2-n)%24==0 \\ _Charles R Greathouse IV_, Oct 16 2015
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_, Aug 23 2009
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