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Numbers that are congruent to {0, 1, 4} mod 8.
3

%I #15 Sep 08 2022 08:44:57

%S 0,1,4,8,9,12,16,17,20,24,25,28,32,33,36,40,41,44,48,49,52,56,57,60,

%T 64,65,68,72,73,76,80,81,84,88,89,92,96,97,100,104,105,108,112,113,

%U 116,120,121,124,128,129,132,136,137,140,144,145,148,152,153,156

%N Numbers that are congruent to {0, 1, 4} mod 8.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).

%F G.f.: x^2*(1+3*x+4*x^2)/((1-x)^2*(1+x+x^2)). [_Colin Barker_, May 13 2012]

%F From _Wesley Ivan Hurt_, Jun 10 2016: (Start)

%F a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

%F a(n) = (24*n-33-3*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9.

%F a(3k) = 8k-4, a(3k-1) = 8k-7, a(3k-2) = 8k-8. (End)

%p A047462:=n->(24*n-33-3*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047462(n), n=1..100); # _Wesley Ivan Hurt_, Jun 10 2016

%t Select[Range[0, 150], MemberQ[{0, 1, 4}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 10 2016 *)

%o (Magma) [n : n in [0..150] | n mod 8 in [0, 1, 4]]; // _Wesley Ivan Hurt_, Jun 10 2016

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_