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A047286 Numbers that are congruent to {1, 2, 3, 6} mod 7. 1
1, 2, 3, 6, 8, 9, 10, 13, 15, 16, 17, 20, 22, 23, 24, 27, 29, 30, 31, 34, 36, 37, 38, 41, 43, 44, 45, 48, 50, 51, 52, 55, 57, 58, 59, 62, 64, 65, 66, 69, 71, 72, 73, 76, 78, 79, 80, 83, 85, 86, 87, 90, 92, 93, 94, 97, 99, 100, 101, 104, 106, 107, 108, 111 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

FORMULA

G.f.: x*(1+x+x^2+3*x^3+x^4) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011

From Wesley Ivan Hurt, May 22 2016: (Start)

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

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

a(2n) = A047276(n), a(2n-1) = A047356(n). (End)

E.g.f.: (4 + 3*sin(x) + cos(x) + (7*x - 6)*sinh(x) + (7*x - 5)*cosh(x))/4. - Ilya Gutkovskiy, May 23 2016

MAPLE

A047286:=n->(14*n-11+I^(2*n)+(1+3*I)*I^(-n)+(1-3*I)*I^n)/8: seq(A047286(n), n=1..100); # Wesley Ivan Hurt, May 22 2016

MATHEMATICA

Table[(14n-11+I^(2n)+(1+3I)*I^(-n)+(1-3I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, May 22 2016 *)

LinearRecurrence[{1, 0, 0, 1, -1}, {1, 2, 3, 6, 8}, 80] (* Vincenzo Librandi, May 24 2016 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 7 in [1, 2, 3, 6]]; // Wesley Ivan Hurt, May 22 2016

CROSSREFS

Cf. A047276, A047356.

Sequence in context: A047405 A175904 A084090 * A201822 A093510 A202341

Adjacent sequences:  A047283 A047284 A047285 * A047287 A047288 A047289

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Wesley Ivan Hurt, May 22 2016

STATUS

approved

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Last modified August 24 22:49 EDT 2019. Contains 326314 sequences. (Running on oeis4.)