A047472 Numbers that are congruent to {0, 1, 3} (mod 8).

0, 1, 3, 8, 9, 11, 16, 17, 19, 24, 25, 27, 32, 33, 35, 40, 41, 43, 48, 49, 51, 56, 57, 59, 64, 65, 67, 72, 73, 75, 80, 81, 83, 88, 89, 91, 96, 97, 99, 104, 105, 107, 112, 113, 115, 120, 121, 123, 128, 129, 131, 136, 137, 139, 144, 145, 147, 152, 153, 155

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

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

Programs

Magma

[n : n in [0..150] | n mod 8 in [0, 1, 3]]; // Wesley Ivan Hurt, Jun 09 2016

Maple

A047472:=n->8*n/3-4-cos(2*n*Pi/3)+5*sin(2*n*Pi/3)/(3*sqrt(3)): seq(A047472(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

Mathematica

Select[Range[0, 150], MemberQ[{0, 1, 3}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 09 2016 *)
LinearRecurrence[{1,0,1,-1},{0,1,3,8},60] (* Harvey P. Dale, Aug 31 2024 *)

Formula

Equals partial sums of (0, 1, 2, 5, 1, 2, 5, 1, 2, 5, ...). - Gary W. Adamson, Jun 19 2008

From Colin Barker, Jan 26 2012: (Start)

G.f.: x^2*(1+2*x+5*x^2)/(1-x-x^3+x^4).

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

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

a(n) = 8*n/3 - 4 - cos(2*n*Pi/3) + 5*sin(2*n*Pi/3)/(3*sqrt(3)).

a(3k) = 8k-5, a(3k-1) = 8k-7, a(3k-2) = 8k-8. (End)