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A103215 Numbers congruent to {1, 2, 5, 10, 13, 17} mod 24.

%I A103215 #22 Feb 24 2024 01:10:15
%S A103215 1,2,5,10,13,17,25,26,29,34,37,41,49,50,53,58,61,65,73,74,77,82,85,89,
%T A103215 97,98,101,106,109,113,121,122,125,130,133,137,145,146,149,154,157,
%U A103215 161,169,170,173,178,181,185,193,194,197,202,205,209,217,218,221,226
%N A103215 Numbers congruent to {1, 2, 5, 10, 13, 17} mod 24.
%H A103215 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1).
%F A103215 G.f.: x*(1+x+3*x^2+5*x^3+3*x^4+4*x^5+7*x^6) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - _R. J. Mathar_, Jul 02 2011
%F A103215 a(1)=1, a(2)=2, a(3)=5, a(4)=10, a(5)=13, a(6)=17, a(7)=25, a(n) = a(n-1)+ a(n-6)-a(n-7) for n>7. - _Harvey P. Dale_, Feb 19 2015
%F A103215 From _Wesley Ivan Hurt_, Jul 22 2016: (Start)
%F A103215 a(n) = a(n-6) + 24 for n>6.
%F A103215 a(n) = (12*n - 18 + cos(n*Pi/3) - 3*cos(2*n*Pi/3) - cos(n*Pi) + 2*sqrt(3)*sin(n*Pi/3) + 2*sqrt(3)*sin(2*n*Pi/3))/3.
%F A103215 a(6k) = 24k-7, a(6k-1) = 24k-11, a(6k-2) = 24k-14, a(6k-3) = 24k-19, a(6k-4) = 24k-22, a(6k-5) = 24k-23. (End)
%p A103215 A103215:=n->24*floor(n/6)+[1, 2, 5, 10, 13, 17][(n mod 6)+1]: seq(A103215(n), n=0..100); # _Wesley Ivan Hurt_, Jul 22 2016
%t A103215 Select[Range[300], MemberQ[{1,2,5,10,13,17}, Mod[#,24]]&] (* or *) LinearRecurrence[{1,0,0,0,0,1,-1}, {1,2,5,10,13,17,25}, 60] (* _Harvey P. Dale_, Feb 19 2015 *)
%o A103215 (Haskell)
%o A103215 a103215 n = a103215_list !! (n-1)
%o A103215 a103215_list = [1,2,5,10,13,17] ++ map (+ 24) a103215_list
%o A103215 -- _Reinhard Zumkeller_, Jul 05 2013
%o A103215 (Magma) [n : n in [0..300] | n mod 24 in [1, 2, 5, 10, 13, 17]]; // _Wesley Ivan Hurt_, Jul 22 2016
%Y A103215 Union of A008784 and A103216.
%Y A103215 Cf. A054895.
%K A103215 nonn,easy
%O A103215 1,2
%A A103215 _Ralf Stephan_, Jan 28 2005