A047475 Numbers that are congruent to {1, 2, 3} mod 8.

1, 2, 3, 9, 10, 11, 17, 18, 19, 25, 26, 27, 33, 34, 35, 41, 42, 43, 49, 50, 51, 57, 58, 59, 65, 66, 67, 73, 74, 75, 81, 82, 83, 89, 90, 91, 97, 98, 99, 105, 106, 107, 113, 114, 115, 121, 122, 123, 129, 130, 131, 137, 138, 139, 145, 146, 147, 153, 154, 155

Offset

1,2

Links

Table of n, a(n) for n=1..60.

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

Formula

G.f.: x*(1+x+x^2+5*x^3)/((1-x)^2*(1+x+x^2)). [Colin Barker, May 13 2012]

a(n) = 1+8*floor((n-1)/3)+((n-1) mod 3). - Alois P. Heinz, May 13 2012

From Wesley Ivan Hurt, Jun 10 2016: (Start)

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

a(n) = (24*n-30-15*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 8k-5, a(3k-1) = 8k-6, a(3k-2) = 8k-7. (End)

Maple

A047475:=n->(24*n-30-15*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047475(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Flatten[#+{1, 2, 3}&/@(8*Range[0, 20])] (* or *) LinearRecurrence[{1, 0, 1, -1}, {1, 2, 3, 9}, 70] (* Harvey P. Dale, Nov 06 2013 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [1..3]]; // Wesley Ivan Hurt, Jun 10 2016

Crossrefs

Sequence in context: A309348 A270886 A133557 * A291610 A285428 A039012

Adjacent sequences: A047472 A047473 A047474 * A047476 A047477 A047478

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved