A047491 Numbers that are congruent to {4, 5, 7} mod 8.

4, 5, 7, 12, 13, 15, 20, 21, 23, 28, 29, 31, 36, 37, 39, 44, 45, 47, 52, 53, 55, 60, 61, 63, 68, 69, 71, 76, 77, 79, 84, 85, 87, 92, 93, 95, 100, 101, 103, 108, 109, 111, 116, 117, 119, 124, 125, 127, 132, 133, 135, 140, 141, 143, 148, 149, 151, 156, 157

Offset

1,1

Links

Table of n, a(n) for n=1..59.

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

Formula

G.f.: x*(4+x+2*x^2+x^3)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Nov 06 2015

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-9*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 8k-1, a(3k-1) = 8k-3, a(3k-2) = 8k-4. (End)

Maple

A047491:=n->(24*n-9*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047491(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

Mathematica

Select[Range[0, 150], MemberQ[{4, 5, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 09 2016 *)
LinearRecurrence[{1, 0, 1, -1}, {4, 5, 7, 12}, 60] (* Harvey P. Dale, Feb 06 2019 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [4, 5, 7]]; // Wesley Ivan Hurt, Jun 09 2016

Crossrefs

Sequence in context: A129302 A216536 A051658 * A064401 A079337 A160934

Adjacent sequences: A047488 A047489 A047490 * A047492 A047493 A047494

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved