A103215 Numbers congruent to {1, 2, 5, 10, 13, 17} mod 24.
1, 2, 5, 10, 13, 17, 25, 26, 29, 34, 37, 41, 49, 50, 53, 58, 61, 65, 73, 74, 77, 82, 85, 89, 97, 98, 101, 106, 109, 113, 121, 122, 125, 130, 133, 137, 145, 146, 149, 154, 157, 161, 169, 170, 173, 178, 181, 185, 193, 194, 197, 202, 205, 209, 217, 218, 221, 226
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).
Programs
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Haskell
a103215 n = a103215_list !! (n-1) a103215_list = [1,2,5,10,13,17] ++ map (+ 24) a103215_list -- Reinhard Zumkeller, Jul 05 2013
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Magma
[n : n in [0..300] | n mod 24 in [1, 2, 5, 10, 13, 17]]; // Wesley Ivan Hurt, Jul 22 2016
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Maple
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
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Mathematica
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 *)
Formula
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
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
From Wesley Ivan Hurt, Jul 22 2016: (Start)
a(n) = a(n-6) + 24 for n>6.
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.
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)