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A032775 Numbers that are congruent to {0, 1, 2, 3, 5, 6} mod 7. 4
0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 80, 82, 83 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

n(n+1)(n+2)...(n+6) / (n + (n+1) + (n+2) + ... + (n+6)) is an integer.

LINKS

Table of n, a(n) for n=1..72.

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

FORMULA

Natural numbers minus '4, 11, 18, 25, ...' (= previous term + 7).

a(n) = -1 + Sum_{k=1..n} ((1/90)*(22*(k mod 6) - 8*((k+1) mod 6) + 7*((k+2) mod 6) + 7*((k+3) mod 6) + 7*((k+4) mod 6) + 7*((k+5) mod 6)), with n >= 1. - Paolo P. Lava, Sep 03 2010

G.f.: x^2*(1+x+x^2+2*x^3+x^4+x^5) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, Jun 15 2016: (Start)

a(n) = a(n-1) + a(n-6) - a(n-7) for n > 7.

a(n) = (42*n - 45 - 3*cos(n*Pi) + 12*cos(n*Pi/3) - 4*sqrt(3)*sin(2*n*Pi/3))/36.

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

MAPLE

A032775:=n->(42*n-45-3*cos(n*Pi)+12*cos(n*Pi/3)-4*sqrt(3)*sin(2*n*Pi/3))/36: seq(A032775(n), n=1..100); # Wesley Ivan Hurt, Jun 15 2016

MATHEMATICA

Select[Range[0, 100], MemberQ[{0, 1, 2, 3, 5, 6}, Mod[#, 7]] &] (* Wesley Ivan Hurt, Jun 15 2016 *)

DeleteCases[Range[0, 100], _?(Mod[#, 7]==4&)] (* or *) LinearRecurrence[ {1, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 3, 5, 6, 7}, 80] (* Harvey P. Dale, Sep 19 2020 *)

PROG

(MAGMA) [ n: n in [0..90] | n mod 7 in {0, 1, 2, 3, 5, 6} ]; // Vincenzo Librandi, Dec 29 2010

CROSSREFS

Cf. A032774, A032776.

Sequence in context: A183295 A029927 A047334 * A057905 A039253 A193533

Adjacent sequences:  A032772 A032773 A032774 * A032776 A032777 A032778

KEYWORD

nonn,easy

AUTHOR

Patrick De Geest, May 15 1998

STATUS

approved

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Last modified October 20 07:16 EDT 2021. Contains 348099 sequences. (Running on oeis4.)