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A047315 Numbers that are congruent to {2, 4, 5, 6} mod 7. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 24 04:41 EDT 2021. Contains 348217 sequences. (Running on oeis4.)