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A174438 Numbers that are congruent to {0, 2, 5, 8} mod 9. 3

%I

%S 0,2,5,8,9,11,14,17,18,20,23,26,27,29,32,35,36,38,41,44,45,47,50,53,

%T 54,56,59,62,63,65,68,71,72,74,77,80,81,83,86,89,90,92,95,98,99,101,

%U 104,107,108,110,113,116,117,119,122,125,126,128,131,134,135,137

%N Numbers that are congruent to {0, 2, 5, 8} mod 9.

%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) = 3*(n-floor(n/4))-(3-I^n-(-I)^n-(-1)^n)/4 where I=sqrt(-1), offset=0.

%F From _Wesley Ivan Hurt_, Jun 07 2016: (Start)

%F G.f.: x^2*(2+3*x+3*x^2+x^3)/((x-1)^2*(1+x+x^2+x^3)).

%F a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

%F a(n) = (18*n-15+i^(2*n)+(3-i)*i^(-n)+(3+i)*i^n)/8 where i=sqrt(-1). (End)

%p seq(3*(n-floor(n/4))-(3-I^n-(-I)^n-(-1)^n)/4, n=0..100);

%t Table[(18n-15+I^(2n)+(3-I)*I^(-n)+(3+I)*I^n)/8, {n, 80}] (* _Wesley Ivan Hurt_, Jun 07 2016 *)

%t Select[Range[0,150],MemberQ[{0,2,5,8},Mod[#,9]]&] (* _Harvey P. Dale_, Jan 02 2019 *)

%o (MAGMA) [n : n in [0..150] | n mod 9 in [0, 2, 5, 8]]; // _Wesley Ivan Hurt_, Jun 07 2016

%K nonn,easy

%O 1,2

%A _Gary Detlefs_, Mar 19 2010

%E a(23) corrected by _Chai Wah Wu_, Jun 10 2016

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Last modified September 26 21:46 EDT 2020. Contains 337377 sequences. (Running on oeis4.)