A047329 Numbers that are congruent to {1, 3, 5, 6} mod 7.

1, 3, 5, 6, 8, 10, 12, 13, 15, 17, 19, 20, 22, 24, 26, 27, 29, 31, 33, 34, 36, 38, 40, 41, 43, 45, 47, 48, 50, 52, 54, 55, 57, 59, 61, 62, 64, 66, 68, 69, 71, 73, 75, 76, 78, 80, 82, 83, 85, 87, 89, 90, 92, 94, 96, 97, 99, 101, 103, 104, 106, 108, 110, 111

Offset

1,2

References

Robert Fludd, Utriusque Cosmi ... Historia, Oppenheim, 1617-1619.

Links

Table of n, a(n) for n=1..64.

Robert Fludd, Page 158 of "Utriusque Cosmi" in Beinecke Rare Book and Manuscript Library Photonegatives Collection.

Robert Fludd, Larger version of the same image

Robert Fludd, Utriusque Cosmi, Maioris scilicet et Minoris, metaphysica, physica, atque technica Historia, available as ZIP or PDF download.

Wikipedia, Robert Fludd

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

Formula

a(n) = floor((7n-1)/4). - Gary Detlefs, Mar 07 2010

G.f.: (x*(1+2*x+2*x^2+x^3+x^4)) / ((1+x)*(x^2+1)*(x-1)^2). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, May 21 2016: (Start)

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

a(n) = (14n-5-i^(2n)-(1+i)*i^(-n)-(1-i)*i^n)/8 where i=sqrt(-1).

a(2n) = A047280(n), a(2n-1) = A047383(n). (End)

E.g.f.: (4 - sin(x) - cos(x) + (7*x - 2)*sinh(x) + (7*x - 3)*cosh(x))/4. - Ilya Gutkovskiy, May 21 2016

Maple

A047329:=n->floor((7*n-1)/4): seq(A047329(n), n=1..100); # Wesley Ivan Hurt, May 21 2016

Mathematica

Table[Floor[(7*n-1)/4], {n, 80}] (* Wesley Ivan Hurt, May 21 2016 *)
#+{1, 3, 5, 6}&/@(7*Range[0, 20])//Flatten (* Harvey P. Dale, Jan 07 2021 *)

Prog

(Haskell)
a047329 n = a047329_list !! (n-1)
a047329_list = [1, 3, 5, 6] ++ map (+ 7) a047329_list
-- Reinhard Zumkeller, Jan 07 2014
(Magma) [Floor((7*n-1)/4) : n in [1..100]]; // Wesley Ivan Hurt, May 21 2016

Crossrefs

Cf. A047280, A047383, A082977.

Sequence in context: A292646 A022838 A329841 * A187685 A300730 A191777

Adjacent sequences: A047326 A047327 A047328 * A047330 A047331 A047332

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Fludd reference from Brendan McKay, May 27 2003

More terms from Wesley Ivan Hurt, May 21 2016

Status

approved