A047298 Numbers that are congruent to {1, 3, 4, 6} mod 7.

1, 3, 4, 6, 8, 10, 11, 13, 15, 17, 18, 20, 22, 24, 25, 27, 29, 31, 32, 34, 36, 38, 39, 41, 43, 45, 46, 48, 50, 52, 53, 55, 57, 59, 60, 62, 64, 66, 67, 69, 71, 73, 74, 76, 78, 80, 81, 83, 85, 87, 88, 90, 92, 94, 95, 97, 99, 101, 102, 104, 106, 108, 109, 111

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A047280, A047346.

Programs

Magma

[n : n in [0..150] | n mod 7 in [1, 3, 4, 6]]; // Wesley Ivan Hurt, May 22 2016

Maple

A047298:=n->I^(-n)*(I-1-7*I^n+14*n*I^n-(1+I)*I^(2*n)+I^(-n))/8: seq(A047298(n), n=1..100); # Wesley Ivan Hurt, May 22 2016

Mathematica

Table[I^(-n)*(I-1-7I^n+14n*I^n-(1+I)*I^(2n)+I^(-n))/8, {n, 80}] (* Wesley Ivan Hurt, May 22 2016 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {1, 3, 4, 6, 8}, 80] (* Vincenzo Librandi, May 24 2016 *)

Formula

a(n) = ceiling(ceiling((7n + 2)/2)/2).

G.f.: x*(1+2*x+x^2+2*x^3+x^4) / ( (1+x)*(x^2+1)*(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) = i^(-n)*(i-1-7*i^n+14*n*i^n-(1+i)*i^(2n)+i^(-n))/8 where i=sqrt(-1).

a(2n) = A047280(n), a(2n-1) = A047346(n). (End)

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

Extensions

More terms from Wesley Ivan Hurt, May 22 2016