A047559 Numbers that are congruent to {0, 1, 3, 6, 7} mod 8.

0, 1, 3, 6, 7, 8, 9, 11, 14, 15, 16, 17, 19, 22, 23, 24, 25, 27, 30, 31, 32, 33, 35, 38, 39, 40, 41, 43, 46, 47, 48, 49, 51, 54, 55, 56, 57, 59, 62, 63, 64, 65, 67, 70, 71, 72, 73, 75, 78, 79, 80, 81, 83, 86, 87, 88, 89, 91, 94, 95, 96, 97, 99, 102, 103, 104

Offset

1,3

Links

Table of n, a(n) for n=1..66.

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

Formula

a(0)=0, a(1)=1, a(2)=3, 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, Mar 04 2015

From Wesley Ivan Hurt, Jul 25 2016: (Start)

G.f.: x^2*(1+2*x+3*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 - 35 + 3*(n mod 5) - 7*((n+1) mod 5) - 2*((n+2) mod 5) + 3*((n+3) mod 5) + 3*((n+4) mod 5))/25.

a(5k) = 8k-1, a(5k-1) = 8k-2, a(5k-2) = 8k-5, a(5k-3) = 8k-7, a(5k-4) = 8k-8. (End)

Maple

A047559:=n->8*floor(n/5)+[0, 1, 3, 6, 7][(n mod 5)+1]: seq(A047559(n), n=0..100); # Wesley Ivan Hurt, Jul 25 2016

Mathematica

Select[Range[0, 100], MemberQ[{0, 1, 3, 6, 7}, Mod[#, 8]]&] (* or *) LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 1, 3, 6, 7, 8}, 80] (* Harvey P. Dale, Mar 04 2015 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 1, 3, 6, 7]]; // Wesley Ivan Hurt, Jul 25 2016

Crossrefs

Sequence in context: A030781 A073417 A299493 * A288742 A113826 A376588

Adjacent sequences: A047556 A047557 A047558 * A047560 A047561 A047562

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved