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

%I #17 Nov 16 2018 22:39:45

%S 0,1,3,5,7,8,9,11,13,15,16,17,19,21,23,24,25,27,29,31,32,33,35,37,39,

%T 40,41,43,45,47,48,49,51,53,55,56,57,59,61,63,64,65,67,69,71,72,73,75,

%U 77,79,80,81,83,85,87,88,89

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

%C Also nonnegative integers primitively represented by x^2 - y^2. - _Ray Chandler_, Aug 23 2014

%H Ray Chandler, <a href="/A047486/b047486.txt">Table of n, a(n) for n = 1..10000</a>

%H N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)

%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^2 + 1)*(1 + x)^2/((x^4 + x^3 + x^2 + x + 1)*(x - 1)^2). - _R. J. Mathar_, Oct 07 2011

%F From _Wesley Ivan Hurt_, Dec 28 2016: (Start)

%F a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6.

%F a(n) = (40*n - 40 - 2*(n mod 5) - 2*((n+1) mod 5) - 2*((n+2) mod 5) + 3*((n+3) mod 5) + 3*((n+4) mod 5))/25. (End)

%Y Cf. A065091, A094572.

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_