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

1,2

Links

Table of n, a(n) for n=1..58.

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

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)

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 *)

Prog

(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

Crossrefs

Union of A008784 and A103216.

Cf. A054895.

Sequence in context: A180161 A349243 A099261 * A037942 A008784 A224450

Adjacent sequences: A103212 A103213 A103214 * A103216 A103217 A103218

Keyword

nonn,easy

Author

Ralf Stephan, Jan 28 2005

Status

approved