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A047297 Numbers that are congruent to {0, 3, 4, 6} mod 7. 1
0, 3, 4, 6, 7, 10, 11, 13, 14, 17, 18, 20, 21, 24, 25, 27, 28, 31, 32, 34, 35, 38, 39, 41, 42, 45, 46, 48, 49, 52, 53, 55, 56, 59, 60, 62, 63, 66, 67, 69, 70, 73, 74, 76, 77, 80, 81, 83, 84, 87, 88, 90, 91, 94, 95, 97, 98, 101, 102, 104, 105, 108, 109, 111 (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

G.f.: x^2*(3+x+2*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-9+3*i^(2*n)-(1+i)*i^(-n)-(1-i)*i^n)/8 where i=sqrt(-1).

a(2k) = A047280(k), a(2k-1) = A047345(k). (End)

MAPLE

A047297:=n->(14*n-9+3*I^(2*n)-(1+I)*I^(-n)-(1-I)*I^n)/8: seq(A047297(n), n=1..100); # Wesley Ivan Hurt, Jun 02 2016

MATHEMATICA

Table[(14n-9+3*I^(2n)-(1+I)*I^(-n)-(1-I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, Jun 02 2016 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 7 in [0, 3, 4, 6]]; // Wesley Ivan Hurt, Jun 02 2016

CROSSREFS

Cf. A047280, A047345.

Sequence in context: A093579 A060832 A341292 * A183233 A191926 A065135

Adjacent sequences:  A047294 A047295 A047296 * A047298 A047299 A047300

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified May 16 12:54 EDT 2021. Contains 343947 sequences. (Running on oeis4.)