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

%I

%S 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,

%T 30,31,32,33,35,36,37,38,39,40,41,43,44,45,46,47,48,49,51,52,53,54,55,

%U 56,57,59,60,61,62,63,64,65,67,68,69,70,71,72,73,75,76,77

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

%H G. C. Greubel, <a href="/A047565/b047565.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,1,-1).

%F From _Chai Wah Wu_, May 30 2016: (Start)

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

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

%F From _Wesley Ivan Hurt_, Jul 21 2016: (Start)

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

%F 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.

%F 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)

%p 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

%t LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 1, 3, 4, 5, 6, 7, 8} ,50] (* _G. C. Greubel_, May 30 2016 *)

%t Select[Range[0,200], MemberQ[{0, 1, 3, 4, 5, 6, 7}, Mod[#, 8] &]] (* _Vincenzo Librandi_, May 30 2016 *)

%o (MAGMA) [n: n in [0..150] | n mod 8 in [0,1,3,4,5,6,7]]; // _Vincenzo Librandi_, May 30 2016

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_

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Last modified July 29 11:53 EDT 2021. Contains 346346 sequences. (Running on oeis4.)