A047315 - OEIS

A047315

Numbers that are congruent to {2, 4, 5, 6} mod 7.

2, 4, 5, 6, 9, 11, 12, 13, 16, 18, 19, 20, 23, 25, 26, 27, 30, 32, 33, 34, 37, 39, 40, 41, 44, 46, 47, 48, 51, 53, 54, 55, 58, 60, 61, 62, 65, 67, 68, 69, 72, 74, 75, 76, 79, 81, 82, 83, 86, 88, 89, 90, 93, 95, 96, 97, 100, 102, 103, 104, 107, 109, 110, 111

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OFFSET

1,1

LINKS

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

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

FORMULA

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

From Wesley Ivan Hurt, Jun 03 2016: (Start)

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

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

a(2k) = A047288(k), a(2k-1) = A047385(k). (End)

MAPLE

A047315:=n->(14*n-1-I^(2*n)-(3-I)*I^(-n)-(3+I)*I^n)/8: seq(A047315(n), n=1..100); # Wesley Ivan Hurt, Jun 03 2016

MATHEMATICA

Table[(14n-1-I^(2n)-(3-I)*I^(-n)-(3+I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, Jun 03 2016 *)

Select[Range[200], MemberQ[{2, 4, 5, 6}, Mod[#, 7]]&] (* or *) LinearRecurrence[ {1, 0, 0, 1, -1}, {2, 4, 5, 6, 9}, 100] (* Harvey P. Dale, Jan 19 2019 *)

PROG

(Magma) [n : n in [0..150] | n mod 7 in [2, 4, 5, 6]]; // Wesley Ivan Hurt, Jun 03 2016

CROSSREFS

Cf. A047288, A047385.

Sequence in context: A231587 A050011 A030303 * A125881 A287370 A089969

Adjacent sequences: A047312 A047313 A047314 * A047316 A047317 A047318

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved