A047373 Numbers that are congruent to {0, 1, 2, 3, 5} mod 7.

0, 1, 2, 3, 5, 7, 8, 9, 10, 12, 14, 15, 16, 17, 19, 21, 22, 23, 24, 26, 28, 29, 30, 31, 33, 35, 36, 37, 38, 40, 42, 43, 44, 45, 47, 49, 50, 51, 52, 54, 56, 57, 58, 59, 61, 63, 64, 65, 66, 68, 70, 71, 72, 73, 75, 77, 78, 79, 80, 82, 84, 85, 86, 87, 89, 91, 92

Offset

1,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

G.f.: x^2*(1+x+x^2+2*x^3+2*x^4)/ ( (x^4+x^3+x^2+x+1)*(x-1)^2 ). - R. J. Mathar, Dec 04 2011

From Wesley Ivan Hurt, Aug 08 2016: (Start)

a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6.

a(n) = a(n-5) + 7 for n > 5.

a(n) = (35*n - 50 - 3*(n mod 5) + 2*((n+1) mod 5) + 2*((n+2) mod 5) + 2*((n+3) mod 5) - 3*((n+4) mod 5))/25.

a(5*k) = 7*k-2, a(5*k-1) = 7*k-4, a(5*k-2) = 7*k-5, a(5*k-3) = 7*k-6, a(5*k-4) = 7*k-7. (End)

Maple

A047373:=n->7*floor(n/5)+[(0, 1, 2, 3, 5)][(n mod 5)+1]: seq(A047373(n), n=0..100); # Wesley Ivan Hurt, Aug 08 2016

Mathematica

Select[Range[0, 100], MemberQ[{0, 1, 2, 3, 5}, Mod[#, 7]] &] (* Wesley Ivan Hurt, Aug 08 2016 *)
LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 1, 2, 3, 5, 7}, 100] (* Vincenzo Librandi, Aug 08 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 7 in [0, 1, 2, 3, 5]]; // Wesley Ivan Hurt, Aug 08 2016

Crossrefs

Sequence in context: A055977 A180221 A111292 * A039048 A105764 A226811

Adjacent sequences: A047370 A047371 A047372 * A047374 A047375 A047376

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved