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A047312 Numbers that are congruent to {0, 4, 5, 6} mod 7. 1
0, 4, 5, 6, 7, 11, 12, 13, 14, 18, 19, 20, 21, 25, 26, 27, 28, 32, 33, 34, 35, 39, 40, 41, 42, 46, 47, 48, 49, 53, 54, 55, 56, 60, 61, 62, 63, 67, 68, 69, 70, 74, 75, 76, 77, 81, 82, 83, 84, 88, 89, 90, 91, 95, 96, 97, 98, 102, 103, 104, 105, 109, 110, 111 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

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

FORMULA

G.f.: x^2*(4+x+x^2+x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 25 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-5+3*i^(2*n)-(3+3*i)*i^(-n)-(3-3*i)*i^n)/8 where i=sqrt(-1).

a(2k) = A047288(k), a(2k-1) = A047382(k). (End)

MAPLE

A047312:=n->(14*n-5+3*I^(2*n)-(3+3*I)*I^(-n)-(3-3*I)*I^n)/8: seq(A047312(n), n=1..100); # Wesley Ivan Hurt, Jun 03 2016

MATHEMATICA

Table[(14n-5+3*I^(2n)-(3+3*I)*I^(-n)-(3-3*I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, Jun 03 2016 *)

PROG

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

CROSSREFS

Cf. A047288, A047382.

Sequence in context: A139448 A022561 A213524 * A191164 A004714 A254713

Adjacent sequences:  A047309 A047310 A047311 * A047313 A047314 A047315

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 22 02:46 EST 2022. Contains 350481 sequences. (Running on oeis4.)