A047565 Numbers that are congruent to {0, 1, 3, 4, 5, 6, 7} mod 8.

0, 1, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

Formula

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

G.f.: x^2*(x^6 + x^5 + x^4 + x^3 + x^2 + 2*x + 1)/(x^8 - x^7 - x + 1).

a(n) = a(n-1) + a(n-7) - a(n-8) for n>8. (End)

From Wesley Ivan Hurt, Jul 21 2016: (Start)

a(n) = a(n-7) + 8 for n>7.

a(n) = (56*n - 42 + (n mod 7) + ((n+1) mod 7) + ((n+2) mod 7) + ((n+3) mod 7) - 6*((n+4) mod 7) + ((n+5) mod 7) + ((n+6) mod 7))/49.

a(7*k) = 8*k-1, a(7*k-1) = 8*k-2, a(7*k-2) = 8*k-3, a(7*k-3) = 8*k-4, a(7*k-4) = 8*k-5, a(7*k-5) = 8*k-7, a(7*k-6) = 8*k-8. (End)

Maple

A047565:=n->8*floor(n/7)+[0, 1, 3, 4, 5, 6, 7][(n mod 7)+1]: seq(A047565(n), n=0..100); # Wesley Ivan Hurt, Jul 21 2016

Mathematica

LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 1, 3, 4, 5, 6, 7, 8} , 50] (* G. C. Greubel, May 30 2016 *)
Select[Range[0, 200], MemberQ[{0, 1, 3, 4, 5, 6, 7}, Mod[#, 8] &]] (* Vincenzo Librandi, May 30 2016 *)

Prog

(Magma) [n: n in [0..150] | n mod 8 in [0, 1, 3, 4, 5, 6, 7]]; // Vincenzo Librandi, May 30 2016

Crossrefs

Sequence in context: A137937 A260580 A297468 * A026466 A304806 A304810

Adjacent sequences: A047562 A047563 A047564 * A047566 A047567 A047568

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved