A047286 Numbers that are congruent to {1, 2, 3, 6} mod 7.

1, 2, 3, 6, 8, 9, 10, 13, 15, 16, 17, 20, 22, 23, 24, 27, 29, 30, 31, 34, 36, 37, 38, 41, 43, 44, 45, 48, 50, 51, 52, 55, 57, 58, 59, 62, 64, 65, 66, 69, 71, 72, 73, 76, 78, 79, 80, 83, 85, 86, 87, 90, 92, 93, 94, 97, 99, 100, 101, 104, 106, 107, 108, 111

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

G.f.: x*(1+x+x^2+3*x^3+x^4) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011

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

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(n) = (14n-11+i^(2n)+(1+3i)*i^(-n)+(1-3i)*i^n)/8 where i=sqrt(-1).

a(2n) = A047276(n), a(2n-1) = A047356(n). (End)

E.g.f.: (4 + 3*sin(x) + cos(x) + (7*x - 6)*sinh(x) + (7*x - 5)*cosh(x))/4. - Ilya Gutkovskiy, May 23 2016

Maple

A047286:=n->(14*n-11+I^(2*n)+(1+3*I)*I^(-n)+(1-3*I)*I^n)/8: seq(A047286(n), n=1..100); # Wesley Ivan Hurt, May 22 2016

Mathematica

Table[(14n-11+I^(2n)+(1+3I)*I^(-n)+(1-3I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, May 22 2016 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {1, 2, 3, 6, 8}, 80] (* Vincenzo Librandi, May 24 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 7 in [1, 2, 3, 6]]; // Wesley Ivan Hurt, May 22 2016

Crossrefs

Cf. A047276, A047356.

Sequence in context: A175904 A084090 A353988 * A344156 A344166 A201822

Adjacent sequences: A047283 A047284 A047285 * A047287 A047288 A047289

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Wesley Ivan Hurt, May 22 2016

Status

approved