A047536 Numbers that are congruent to {0, 4, 7} mod 8.

0, 4, 7, 8, 12, 15, 16, 20, 23, 24, 28, 31, 32, 36, 39, 40, 44, 47, 48, 52, 55, 56, 60, 63, 64, 68, 71, 72, 76, 79, 80, 84, 87, 88, 92, 95, 96, 100, 103, 104, 108, 111, 112, 116, 119, 120, 124, 127, 128, 132, 135, 136, 140, 143, 144, 148, 151, 152, 156, 159

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

Formula

From Chai Wah Wu, May 29 2016: (Start)

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

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

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

a(n) = (24*n-15+6*cos(2*n*Pi/3)-4*sqrt(3)*sin(2*n*Pi/3))/9.

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

Maple

A047536:=n->(24*n-15+6*cos(2*n*Pi/3)-4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047536(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

LinearRecurrence[{1, 0, 1, -1}, {0, 4, 7, 8}, 50] (* G. C. Greubel, May 29 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 4, 7]]; // Wesley Ivan Hurt, May 29 2016

Crossrefs

Sequence in context: A162967 A070286 A324978 * A093494 A310934 A310935

Adjacent sequences: A047533 A047534 A047535 * A047537 A047538 A047539

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved