A047283 Numbers that are congruent to {0, 1, 3, 6} mod 7.

0, 1, 3, 6, 7, 8, 10, 13, 14, 15, 17, 20, 21, 22, 24, 27, 28, 29, 31, 34, 35, 36, 38, 41, 42, 43, 45, 48, 49, 50, 52, 55, 56, 57, 59, 62, 63, 64, 66, 69, 70, 71, 73, 76, 77, 78, 80, 83, 84, 85, 87, 90, 91, 92, 94, 97, 98, 99, 101, 104, 105, 106, 108, 111

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A047336, A047355.

Programs

Magma

[n : n in [0..150] | n mod 7 in [0, 1, 3, 6]]; // Wesley Ivan Hurt, May 22 2016

Maple

A047283:=n->(14*n-15+I^(2*n)+(3+I)*I^(-n)+(3-I)*I^n)/8: seq(A047283(n), n=1..100); # Wesley Ivan Hurt, May 22 2016

Mathematica

Select[Range[0,100], MemberQ[{0,1,3,6}, Mod[#,7]]&] (* or *) LinearRecurrence[{1,0,0,1,-1}, {0,1,3,6,7}, 60] (* Harvey P. Dale, Mar 09 2012 *)

Formula

G.f.: x^2*(1+2*x+3*x^2+x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. - Harvey P. Dale, Mar 09 2012

From Wesley Ivan Hurt, May 22 2016: (Start)

a(n) = (14n-15+i^(2n)+(3+i)*i^(-n)+(3-i)*i^n)/8 where i=sqrt(-1).

a(2n) = A047336(n), a(2n-1) = A047355(n). (End)

Extensions

More terms from Wesley Ivan Hurt, May 22 2016