A047469 Numbers that are congruent to {0, 1, 2} mod 8.

0, 1, 2, 8, 9, 10, 16, 17, 18, 24, 25, 26, 32, 33, 34, 40, 41, 42, 48, 49, 50, 56, 57, 58, 64, 65, 66, 72, 73, 74, 80, 81, 82, 88, 89, 90, 96, 97, 98, 104, 105, 106, 112, 113, 114, 120, 121, 122, 128, 129, 130, 136, 137, 138, 144, 145, 146, 152, 153, 154

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A030341.

Cf. similar sequences with formula n+i*floor(n/3) listed in A281899.

Programs

Magma

[n : n in [0..150] | n mod 8 in [0..2]]; // Wesley Ivan Hurt, Jun 09 2016

Maple

A047469:=n->(24*n-39-15*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047469(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

Mathematica

Select[Range[0, 150], MemberQ[{0, 1, 2}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 09 2016 *)

PARI

a(n)=n+(n-1)\3*5-1

Formula

G.f.: x*(1 + x + 6*x^2)/((1 - x)*(1 - x^3)).

a(n+1) = Sum_{k>=0} A030341(n,k)*b(k) with b(0)=1 and b(k) = 8*3^(k-1) for k>0. - Philippe Deléham, Oct 24 2011

From Wesley Ivan Hurt, Jun 09 2016: (Start)

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

a(n) = (24*n-39-15*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 8k-6, a(3k-1) = 8k-7, a(3k-2) = 8k-8. (End)

a(n) = n + 5*floor((n-1)/3) - 1. - Bruno Berselli, Feb 06 2017