|
%I #21 Sep 08 2022 08:44:57
%S 0,1,4,5,7,8,9,12,13,15,16,17,20,21,23,24,25,28,29,31,32,33,36,37,39,
%T 40,41,44,45,47,48,49,52,53,55,56,57,60,61,63,64,65,68,69,71,72,73,76,
%U 77,79,80,81,84,85,87,88,89,92,93,95,96,97,100,101,103
%N Numbers that are congruent to {0, 1, 4, 5, 7} mod 8.
%H Vincenzo Librandi, <a href="/A047494/b047494.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).
%F G.f.: x^2*(x^4+2*x^3+x^2+3*x+1)/((x-1)^2*(x^4+x^3+x^2+x+1)). [_Colin Barker_, Jun 22 2012]
%F From _Wesley Ivan Hurt_, Jul 31 2016: (Start)
%F a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6, a(n) = a(n-5) + 8 for n > 5.
%F a(n) = (40*n - 35 - 2*(n mod 5) + 3*((n+1) mod 5) - 7*((n+2) mod 5) + 3*((n+3) mod 5) + 3*((n+4) mod 5))/25.
%F a(5k) = 8k-1, a(5k-1) = 8k-3, a(5k-2) = 8k-4, a(5k-3) = 8k-7, a(5k-4) = 8k-8. (End)
%p A047494:=n->8*floor(n/5)+[(0, 1, 4, 5, 7)][(n mod 5)+1]: seq(A047494(n), n=0..100); # _Wesley Ivan Hurt_, Jul 31 2016
%t Select[Range[0, 100], MemberQ[{0, 1, 4, 5, 7}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jul 31 2016 *)
%t LinearRecurrence[{1,0,0,0,1,-1},{0,1,4,5,7,8},80] (* _Harvey P. Dale_, Jul 02 2021 *)
%o (Magma) [n : n in [0..150] | n mod 8 in [0, 1, 4, 5, 7]]; // _Wesley Ivan Hurt_, Jul 31 2016
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_
|
