A047294 Numbers that are congruent to {1, 2, 4, 6} mod 7.

1, 2, 4, 6, 8, 9, 11, 13, 15, 16, 18, 20, 22, 23, 25, 27, 29, 30, 32, 34, 36, 37, 39, 41, 43, 44, 46, 48, 50, 51, 53, 55, 57, 58, 60, 62, 64, 65, 67, 69, 71, 72, 74, 76, 78, 79, 81, 83, 85, 86, 88, 90, 92, 93, 95, 97, 99, 100, 102, 104, 106, 107, 109, 111

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

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

Formula

a(n) = ceiling(floor((7*n - 5)/2)/2).

From Colin Barker, Mar 14 2012: (Start)

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

G.f.: x*(1 + x + 2*x^2 + 2*x^3 + x^4)/((1-x)^2*(1+x)*(1+x^2)). (End)

a(n) = (-9 -(-1)^n + (1+i)*(-i)^n + (1-i)*i^n + 14*n)/8 where i=sqrt(-1). - Colin Barker, May 14 2012

a(2k) = A047276(k), a(2k-1) = A047346(k). - Wesley Ivan Hurt, Jun 01 2016

E.g.f.: (4 + sin(x) + cos(x) + (7*x - 4)*sinh(x) + (7*x - 5)*cosh(x))/4. - Ilya Gutkovskiy, Jun 01 2016

Maple

A047294:=n->ceil(floor((7*n-5)/2)/2): seq(A047294(n), n=1..100); # Wesley Ivan Hurt, Jun 01 2016

Mathematica

Select[Range[0, 100], MemberQ[{1, 2, 4, 6}, Mod[#, 7]]&] (* Vincenzo Librandi, Apr 27 2012 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {1, 2, 4, 6, 8}, 100] (* G. C. Greubel, Jun 01 2016 *)

Prog

(Magma) I:=[1, 2, 4, 6, 8]; [n le 5 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..70]]; // Vincenzo Librandi, Apr 27 2012
(PARI) x='x+O('x^100); Vec(x*(1+x+2*x^2+2*x^3+x^4)/((1-x)^2*(1+x)*(1+x^2))) \\ Altug Alkan, Dec 24 2015

Crossrefs

Cf. A047276, A047346.

Sequence in context: A050091 A184740 A184638 * A195173 A215000 A228246

Adjacent sequences: A047291 A047292 A047293 * A047295 A047296 A047297

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved