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A047559 Numbers that are congruent to {0, 1, 3, 6, 7} mod 8. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A053030

Adjacent sequences:  A047556 A047557 A047558 * A047560 A047561 A047562

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified March 18 22:11 EDT 2019. Contains 321305 sequences. (Running on oeis4.)