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A047291 Numbers that are congruent to {0, 1, 4, 6} mod 7. 1
0, 1, 4, 6, 7, 8, 11, 13, 14, 15, 18, 20, 21, 22, 25, 27, 28, 29, 32, 34, 35, 36, 39, 41, 42, 43, 46, 48, 49, 50, 53, 55, 56, 57, 60, 62, 63, 64, 67, 69, 70, 71, 74, 76, 77, 78, 81, 83, 84, 85, 88, 90, 91, 92, 95, 97, 98, 99, 102, 104, 105, 106, 109, 111 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

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

FORMULA

From Colin Barker, Mar 13 2012: (Start)

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

G.f.: x^2*(1 + 3*x + 2*x^2 + x^3)/((1-x)^2*(1+x)*(1+x^2)). (End)

a(n) = (-13 - (-1)^n + (3-i)*(-i)^n + (3+i)*i^n + 14*n)/8 where i=sqrt(-1). - Colin Barker, May 14 2012

a(2k) = A047336(k), a(2k-1) = A047345(k). - Wesley Ivan Hurt, Jun 01 2016

E.g.f.: (4 - sin(x) + 3*cos(x) + (7*x - 6)*sinh(x) + 7*(x - 1)*cosh(x))/4. - Ilya Gutkovskiy, Jun 01 2016

MAPLE

A047291:=n->(-13-(-1)^n+(3-I)*(-I)^n+(3+I)*I^n+14*n)/8: seq(A047291(n), n=1..100); # Wesley Ivan Hurt, Jun 01 2016

MATHEMATICA

Select[Range[0, 120], MemberQ[{0, 1, 4, 6}, Mod[#, 7]]&] (* Vincenzo Librandi, Apr 26 2012 *)

LinearRecurrence[{1, 0, 0, 1, -1}, {0, 1, 4, 6, 7}, 100] (* G. C. Greubel, Jun 01 2016 *)

PROG

(MAGMA) I:=[0, 1, 4, 6, 7]; [n le 5 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..70]]; // Vincenzo Librandi, Apr 26 2012

(PARI) x='x+O('x^100); concat(0, Vec(x^2*(1+3*x+2*x^2+x^3)/((1-x)^2*(1+x)*(1+x^2)))) \\ Altug Alkan, Dec 24 2015

CROSSREFS

Cf. A047336, A047345.

Sequence in context: A081712 A178663 A084395 * A100349 A326892 A047507

Adjacent sequences:  A047288 A047289 A047290 * A047292 A047293 A047294

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 1 21:20 EST 2021. Contains 349435 sequences. (Running on oeis4.)