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A047294 Numbers that are congruent to {1, 2, 4, 6} mod 7. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 17 16:56 EDT 2021. Contains 343980 sequences. (Running on oeis4.)