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

Author

Ralf Stephan, Jan 28 2005

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).

Crossrefs

Union of A008784 and A103216.

Cf. A054895.

Programs

Haskell

a103215 n = a103215_list !! (n-1)
a103215_list = [1,2,5,10,13,17] ++ map (+ 24) a103215_list
-- Reinhard Zumkeller, Jul 05 2013

Magma

[n : n in [0..300] | n mod 24 in [1, 2, 5, 10, 13, 17]]; // Wesley Ivan Hurt, Jul 22 2016

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

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)