A047388 Numbers that are congruent to {0, 1, 2, 5} mod 7.

0, 1, 2, 5, 7, 8, 9, 12, 14, 15, 16, 19, 21, 22, 23, 26, 28, 29, 30, 33, 35, 36, 37, 40, 42, 43, 44, 47, 49, 50, 51, 54, 56, 57, 58, 61, 63, 64, 65, 68, 70, 71, 72, 75, 77, 78, 79, 82, 84, 85, 86, 89, 91, 92, 93, 96, 98, 99, 100, 103, 105, 106, 107, 110, 112

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. A047352, A047383.

Programs

Magma

I:=[0, 1, 2, 5, 7]; [n le 5 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..70]]; // Vincenzo Librandi, May 15 2012

Maple

A047388:=n->(-19+I^(2*n)+(1+3*I)*(-I)^n+(1-3*I)*I^n+14*n)/8: seq(A047388(n), n=1..100); # Wesley Ivan Hurt, Jun 01 2016

Mathematica

Select[Range[0,300], MemberQ[{0,1,2,5}, Mod[#,7]]&] (* Vincenzo Librandi, May 15 2012 *)
LinearRecurrence[{1,0,0,1,-1},{0,1,2,5,7},80] (* Harvey P. Dale, Jan 10 2023 *)

PARI

x='x+O('x^100); concat(0, Vec(x^2*(1+x+3*x^2+2*x^3)/((1-x)^2*(1+x)*(1+x^2)))) \\ Altug Alkan, Jun 02 2016

Formula

G.f.: x^2*(1+x+3*x^2+2*x^3)/((1-x)^2*(1+x)*(1+x^2)). - Colin Barker, May 13 2012

a(n) = (-19+(-1)^n+(1+3*i)*(-i)^n+(1-3*i)*i^n+14*n)/8 where i=sqrt(-1). - Colin Barker, May 14 2012

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. - Vincenzo Librandi, May 16 2012

a(2k) = A047383(k), a(2k-1) = A047352(k). - Wesley Ivan Hurt, Jun 01 2016