|
%I #21 Mar 07 2020 08:54:32
%S 1,2,3,5,6,9,10,11,13,14,17,18,19,21,22,25,26,27,29,30,33,34,35,37,38,
%T 41,42,43,45,46,49,50,51,53,54,57,58,59,61,62,65,66,67,69,70,73,74,75,
%U 77,78,81,82,83,85,86,89,90,91,93,94,97,98,99,101,102,105,106
%N Numbers that are primitively represented by x^2 + y^2 + z^2.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1)
%F Numbers that are congruent to {1, 2, 3, 5, 6} mod 8.
%F Union of A047449 and A034045 is A000378. Intersection of A047449 and A034043 is A034046. Numbers that are in A000378 and not congruent to 0 mod 4. - _Ray Chandler_, Sep 05 2004
%F G.f.: x*(1 + x + x^2 + 2*x^3 + x^4 + 2*x^5) / ( (x^4 + x^3 + x^2 + x + 1)*(x-1)^2 ). - _R. J. Mathar_, Dec 07 2011
%F a(n) = a(n-1) + a(n-5) - a(n-6); a(1)=1, a(2)=2, a(3)=3, a(4)=5, a(5)=6, a(6)=9. - _Harvey P. Dale_, Mar 05 2015
%t LinearRecurrence[{1,0,0,0,1,-1},{1,2,3,5,6,9},70] (* _Harvey P. Dale_, Mar 05 2015 *)
%o (PARI) a(n)=(n-1)\5*8+[6,1,2,3,5][n%5+1] \\ _Charles R Greathouse IV_, Jun 11 2015
%Y Cf. A000378, A004215, A034043-A034047.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
|
