A047285 - OEIS

A047285

Numbers that are congruent to {0, 2, 3, 6} mod 7.

0, 2, 3, 6, 7, 9, 10, 13, 14, 16, 17, 20, 21, 23, 24, 27, 28, 30, 31, 34, 35, 37, 38, 41, 42, 44, 45, 48, 49, 51, 52, 55, 56, 58, 59, 62, 63, 65, 66, 69, 70, 72, 73, 76, 77, 79, 80, 83, 84, 86, 87, 90, 91, 93, 94, 97, 98, 100, 101, 104, 105, 107, 108, 111

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OFFSET

1,2

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+3*x^2+x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011

From Wesley Ivan Hurt, Jun 02 2016: (Start)

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

a(n) = (14*n-13+3*i^(2*n)+(1+i)*i^(-n)+(1-i)*i^n)/8 where i=sqrt(-1).

a(2k) = A047276(k), a(2k-1) = A047355(k). (End)

MAPLE

A047285:=n->(14*n-13+3*I^(2*n)+(1+I)*I^(-n)+(1-I)*I^n)/8: seq(A047285(n), n=1..100); # Wesley Ivan Hurt, Jun 02 2016

MATHEMATICA

Table[(14n-13+3*I^(2n)+(1+I)*I^(-n)+(1-I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, Jun 02 2016 *)

Select[Range[0, 120], MemberQ[{0, 2, 3, 6}, Mod[#, 7]]&] (* or *) LinearRecurrence[ {1, 0, 0, 1, -1}, {0, 2, 3, 6, 7}, 100] (* Harvey P. Dale, Jul 12 2020 *)

PROG

(Magma) [n : n in [0..150] | n mod 7 in [0, 2, 3, 6]]; // Wesley Ivan Hurt, Jun 02 2016

CROSSREFS

Cf. A047276, A047355.

Sequence in context: A285567 A153123 A100913 * A191215 A190847 A201734

Adjacent sequences: A047282 A047283 A047284 * A047286 A047287 A047288

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved