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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Programs

Magma

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

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 *)

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)