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

1,3

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^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

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 *)

Prog

(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
(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

Crossrefs

Cf. A047352, A047383.

Sequence in context: A047483 A339309 A167408 * A284529 A191767 A050086

Adjacent sequences: A047385 A047386 A047387 * A047389 A047390 A047391

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved