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A047313 Numbers that are congruent to {1, 4, 5, 6} mod 7. 1
1, 4, 5, 6, 8, 11, 12, 13, 15, 18, 19, 20, 22, 25, 26, 27, 29, 32, 33, 34, 36, 39, 40, 41, 43, 46, 47, 48, 50, 53, 54, 55, 57, 60, 61, 62, 64, 67, 68, 69, 71, 74, 75, 76, 78, 81, 82, 83, 85, 88, 89, 90, 92, 95, 96, 97, 99, 102, 103, 104, 106, 109, 110, 111 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

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

FORMULA

G.f.: x*(1+3*x+x^2+x^3+x^4) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Dec 03 2011

From Wesley Ivan Hurt, May 23 2016: (Start)

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

a(n) = (14n-3+i^(2n)-(3+i)*i^(-n)-(3-i)*i^n)/8 where i=sqrt(-1).

a(2n) = A047288(n), a(2n-1) = A047383(n). (End)

E.g.f.: (4 - sin(x) - 3*cos(x) + (7*x - 2)*sinh(x) + (7*x - 1)*cosh(x))/4. - Ilya Gutkovskiy, May 24 2016

MAPLE

A047313:= n-> iquo(n-1, 4, 'r')*7 +[1, 4, 5, 6][r+1]: seq(A047313(n), n=1..80);  # Alois P. Heinz, Dec 04 2011

MATHEMATICA

Select[Range[100], MemberQ[{1, 4, 5, 6}, Mod[#, 7]]&]  (* Harvey P. Dale, Apr 17 2011 *)

LinearRecurrence[{1, 0, 0, 1, -1}, {1, 4, 5, 6, 8}, 80] (* Jean-Fran├žois Alcover, Feb 18 2016 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 7 in [1, 4, 5, 6]]; // Wesley Ivan Hurt, May 23 2016

CROSSREFS

Cf. A047288, A047383.

Sequence in context: A209722 A035067 A027698 * A030343 A030590 A047430

Adjacent sequences:  A047310 A047311 A047312 * A047314 A047315 A047316

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 24 14:44 EDT 2021. Contains 348233 sequences. (Running on oeis4.)