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%I #14 Sep 08 2022 08:45:38
%S 0,1,16,33,48,49,64,81,96,97,112,129,144,145,160,177,192,193,208,225,
%T 240,241,256,273,288,289,304,321,336,337,352,369,384,385,400,417,432,
%U 433,448,465,480,481,496,513,528,529,544,561,576,577,592,609,624,625,640,657,672
%N Numbers n such that n^2 - n is divisible by 48.
%C Numbers congruent to {0, 1, 16, 33} mod 48. - _Charles R Greathouse IV_, Apr 10 2012
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F From _Colin Barker_, Apr 10 2012: (Start)
%F G.f.: x^2*(1+15*x+17*x^2+15*x^3)/((1-x)^2*(1+x)*(1+x^2)).
%F a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. (End)
%F a(n) = 12*n-(35+3*i^(2*n))/2+(2+2*i)*i^(-n)+(2-2*i)*i^n where i=sqrt(-1). - _Wesley Ivan Hurt_, Jun 07 2016
%p A151981:=n->12*n-(35+3*I^(2*n))/2+(2+2*I)*I^(-n)+(2-2*I)*I^n: seq(A151981(n), n=1..100); # _Wesley Ivan Hurt_, Jun 07 2016
%t Table[12n-(35+3*I^(2*n))/2+(2+2*I)*I^(-n)+(2-2*I)*I^n, {n, 80}] (* _Wesley Ivan Hurt_, Jun 07 2016 *)
%o (PARI) a(n)=n\4*48+[-15, 0, 1, 16][n%4+1] \\ _Charles R Greathouse IV_, Apr 10 2012
%o (Magma) [n : n in [0..800] | n mod 48 in [0, 1, 16, 33]]; // _Wesley Ivan Hurt_, Jun 07 2016
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_, Aug 23 2009
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