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A047380 Numbers that are congruent to {1, 2, 4, 5} mod 7. 6
1, 2, 4, 5, 8, 9, 11, 12, 15, 16, 18, 19, 22, 23, 25, 26, 29, 30, 32, 33, 36, 37, 39, 40, 43, 44, 46, 47, 50, 51, 53, 54, 57, 58, 60, 61, 64, 65, 67, 68, 71, 72, 74, 75, 78, 79, 81, 82, 85, 86, 88, 89, 92, 93, 95, 96, 99, 100, 102, 103, 106, 107, 109, 110 (list; graph; refs; listen; history; text; internal format)
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

a(n) = (1/4)*(6*(n mod 4) + ((n+1) mod 4) + ((n+2) mod 4)) + 7*A002265. - Paolo P. Lava, Nov 05 2007

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

From Wesley Ivan Hurt, May 20 2016: (Start)

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

a(n) = (14*n - 11 - 3*i^(2*n) - (1+i)*i^(-n-1) - (1-i)*i^(n+1))/8 where i=sqrt(-1).

a(2n) = A047385(n), a(2n-1) = A047346(n). (End)

MAPLE

A047380:=n->(14*n-11-3*I^(2*n)-(1+I)*I^(-n-1)-(1-I)*I^(n+1))/8: seq(A047380(n), n=1..100); # Wesley Ivan Hurt, May 20 2016

MATHEMATICA

Table[(14n-11-3I^(2n)-(1+I)I^(-n-1)-(1-I)I^(n+1))/8, {n, 80}] (* Wesley Ivan Hurt, May 20 2016 *)

LinearRecurrence[{1, 0, 0, 1, -1}, {1, 2, 4, 5, 8}, 100] (* Harvey P. Dale, Jun 05 2016 *)

PROG

(PARI) a(n)=(n-1)\4*7+[5, 1, 2, 4][n%4+1] \\ Charles R Greathouse IV, Jun 11 2015

CROSSREFS

Cf. A002265, A047346, A047385.

Sequence in context: A286031 A027883 A201818 * A288214 A117121 A101925

Adjacent sequences:  A047377 A047378 A047379 * A047381 A047382 A047383

KEYWORD

nonn,easy,changed

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified June 12 10:29 EDT 2021. Contains 344946 sequences. (Running on oeis4.)