A047511 Numbers that are congruent to {0, 2, 4, 6, 7} mod 8.

0, 2, 4, 6, 7, 8, 10, 12, 14, 15, 16, 18, 20, 22, 23, 24, 26, 28, 30, 31, 32, 34, 36, 38, 39, 40, 42, 44, 46, 47, 48, 50, 52, 54, 55, 56, 58, 60, 62, 63, 64, 66, 68, 70, 71, 72, 74, 76, 78, 79, 80, 82, 84, 86, 87, 88, 90, 92, 94, 95, 96, 98, 100, 102, 103

Offset

1,2

Links

Table of n, a(n) for n=1..65.

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

Formula

a(0)=0, a(1)=2, a(2)=4, a(3)=6, a(4)=7, a(5)=8, a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6. - Harvey P. Dale, May 09 2014

From Wesley Ivan Hurt, Jul 31 2016: (Start)

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

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

a(n) = (40*n - 25 + 3*(n mod 5) - 2*((n+1) mod 5) - 2*((n+2) mod 5) - 2*((n+3) mod 5) + 3*((n+4) mod 5))/25.

a(5k) = 8k-1, a(5k-1) = 8k-2, a(5k-2) = 8k-4, a(5k-3) = 8k-6, a(5k-4) = 8k-8. (End)

Maple

A047511:=n->8*floor(n/5)+[(0, 2, 4, 6, 7)][(n mod 5)+1]: seq(A047511(n), n=0..100); # Wesley Ivan Hurt, Jul 31 2016

Mathematica

Select[Range[0, 100], MemberQ[{0, 2, 4, 6, 7}, Mod[#, 8]]&] (* or *) LinearRecurrence[ {1, 0, 0, 0, 1, -1}, {0, 2, 4, 6, 7, 8}, 100] (* Harvey P. Dale, May 09 2014 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 2, 4, 6, 7]]; // Wesley Ivan Hurt, Jul 31 2016

Crossrefs

Sequence in context: A039028 A153282 A014661 * A066507 A285140 A015932

Adjacent sequences: A047508 A047509 A047510 * A047512 A047513 A047514

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved