A047479 Numbers that are congruent to {0, 1, 5, 7} mod 8.

0, 1, 5, 7, 8, 9, 13, 15, 16, 17, 21, 23, 24, 25, 29, 31, 32, 33, 37, 39, 40, 41, 45, 47, 48, 49, 53, 55, 56, 57, 61, 63, 64, 65, 69, 71, 72, 73, 77, 79, 80, 81, 85, 87, 88, 89, 93, 95, 96, 97, 101, 103, 104, 105, 109, 111, 112, 113, 117, 119, 120, 121, 125

Offset

1,3

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

From Colin Barker, May 14 2012: (Start)

a(n) = (-7-(-1)^n+(2-i)*(-i)^n+(2+i)*i^n+8*n)/4 where i=sqrt(-1).

G.f.: x^2*(1+4*x+2*x^2+x^3)/((1-x)^2*(1+x)*(1+x^2)). (End)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. - Vincenzo Librandi, May 16 2012

a(2k) = A047522(k), a(2k-1) = A047615(k). - Wesley Ivan Hurt, Jun 01 2016

E.g.f.: (2 - sin(x) + 2*cos(x) + (4*x - 3)*sinh(x) + 4*(x - 1)*cosh(x))/2. - Ilya Gutkovskiy, Jun 02 2016

Sum_{n>=2} (-1)^n/a(n) = (sqrt(2)-1)*Pi/16 + (8-3*sqrt(2))*log(2)/16 + 3*sqrt(2)*log(2+sqrt(2))/8. - Amiram Eldar, Dec 20 2021

Maple

A047479:=n->(-7-I^(2*n)+(2-I)*(-I)^n+(2+I)*I^n+8*n)/4: seq(A047479(n), n=1..100); # Wesley Ivan Hurt, Jun 01 2016

Mathematica

Select[Range[0, 300], MemberQ[{0, 1, 5, 7}, Mod[#, 8]]&] (* Vincenzo Librandi, May 16 2012 *)

Prog

(Magma) I:=[0, 1, 5, 7, 8]; [n le 5 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..70]]; // Vincenzo Librandi, May 16 2012
(PARI) my(x='x+O('x^100)); concat(0, Vec(x^2*(1+4*x+2*x^2+x^3)/((1-x)^2*(1+x)*(1+x^2)))) \\ Altug Alkan, Dec 24 2015

Crossrefs

Cf. A047522, A047615.

Sequence in context: A080644 A309277 A180241 * A080720 A189034 A112250

Adjacent sequences: A047476 A047477 A047478 * A047480 A047481 A047482

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved