A047449 Numbers that are primitively represented by x^2 + y^2 + z^2.

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, 41, 42, 43, 45, 46, 49, 50, 51, 53, 54, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 73, 74, 75, 77, 78, 81, 82, 83, 85, 86, 89, 90, 91, 93, 94, 97, 98, 99, 101, 102, 105, 106

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A000378, A004215, A034043-A034047.

Programs

Mathematica

LinearRecurrence[{1,0,0,0,1,-1},{1,2,3,5,6,9},70] (* Harvey P. Dale, Mar 05 2015 *)

PARI

a(n)=(n-1)\5*8+[6,1,2,3,5][n%5+1] \\ Charles R Greathouse IV, Jun 11 2015

Formula

Numbers that are congruent to {1, 2, 3, 5, 6} mod 8.

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

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

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