A047325 Numbers that are congruent to {1, 2, 5, 6} mod 7.

1, 2, 5, 6, 8, 9, 12, 13, 15, 16, 19, 20, 22, 23, 26, 27, 29, 30, 33, 34, 36, 37, 40, 41, 43, 44, 47, 48, 50, 51, 54, 55, 57, 58, 61, 62, 64, 65, 68, 69, 71, 72, 75, 76, 78, 79, 82, 83, 85, 86, 89, 90, 92, 93, 96, 97, 99, 100, 103, 104, 106, 107, 110, 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. A047276, A047383.

Programs

Magma

[n : n in [0..150] | n mod 7 in [1, 2, 5, 6]]; // Wesley Ivan Hurt, May 23 2016

Maple

A047325:=n->(14*n-7-3*I^(2*n)+(1-I)*I^(-n)+(1+I)*I^n)/8: seq(A047325(n), n=1..100); # Wesley Ivan Hurt, May 23 2016

Mathematica

Table[(14n-7-3*I^(2n)+(1-I)*I^(-n)+(1+I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, May 23 2016 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {1, 2, 5, 6, 8}, 80] (* Vincenzo Librandi, May 24 2016 *)
#+{1,2,5,6}&/@(7*Range[0,20])//Flatten (* Harvey P. Dale, Aug 16 2018 *)

Formula

G.f.: x*(1+x+3*x^2+x^3+x^4) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Dec 04 2011

From Wesley Ivan Hurt, May 23 2016: (Start)

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

a(n) = (14n-7-3*i^(2n)+(1-i)*i^(-n)+(1+i)*i^n)/8 where i=sqrt(-1).

a(2n) = A047276(n), a(2n-1) = A047383(n). (End)

E.g.f.: (4 - sin(x) + cos(x) + (7*x - 2)*sinh(x) + (7*x - 5)*cosh(x))/4. - Ilya Gutkovskiy, May 24 2016

Extensions

More terms from Wesley Ivan Hurt, May 23 2016