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

1,3

Links

Table of n, a(n) for n=1..64.

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

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)

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 *)

Prog

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

Crossrefs

Cf. A047336, A047355.

Sequence in context: A050244 A295566 A266986 * A155932 A298980 A206586

Adjacent sequences: A047280 A047281 A047282 * A047284 A047285 A047286

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Wesley Ivan Hurt, May 22 2016

Status

approved