A047567 Numbers that are congruent to {0, 4, 5, 6, 7} mod 8.

0, 4, 5, 6, 7, 8, 12, 13, 14, 15, 16, 20, 21, 22, 23, 24, 28, 29, 30, 31, 32, 36, 37, 38, 39, 40, 44, 45, 46, 47, 48, 52, 53, 54, 55, 56, 60, 61, 62, 63, 64, 68, 69, 70, 71, 72, 76, 77, 78, 79, 80, 84, 85, 86, 87, 88, 92, 93, 94, 95, 96, 100, 101, 102, 103

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 (1,0,0,0,1,-1).

Formula

From Chai Wah Wu, May 30 2016: (Start)

a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6.

G.f.: x^2*(x^4 + x^3 + x^2 + x + 4)/(x^6 - x^5 - x + 1). (End)

From Wesley Ivan Hurt, Aug 16 2016: (Start)

a(n) = a(n-5) + 8 for n > 5.

a(n) = n + 2 + 3*floor((n-2)/5).

a(n) = (8*n + 4 - 3*((n+3) mod 5))/5.

a(5k) = 8k-1, a(5k-1) = 8k-2, a(5k-2) = 8k-3, a(5k-3) = 8k-4, a(5k-4) = 8k-8. (End)

Maple

A047567:=n->8*floor(n/5)+[0, 4, 5, 6, 7][(n mod 5)+1]: seq(A047567(n), n=0..100); # Wesley Ivan Hurt, Aug 16 2016

Mathematica

Select[Range[0, 100], MemberQ[{0, 4, 5, 6, 7}, Mod[#, 8]]&] (* Harvey P. Dale, Apr 16 2014 *)
LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 4, 5, 6, 7, 8}, 50] (* G. C. Greubel, May 30 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 4, 5, 6, 7]]; // Wesley Ivan Hurt, Aug 16 2016

Crossrefs

Sequence in context: A285429 A073073 A213525 * A050038 A285218 A059709

Adjacent sequences: A047564 A047565 A047566 * A047568 A047569 A047570

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved