A047456 Numbers that are congruent to {0, 2, 3, 4} mod 8.

0, 2, 3, 4, 8, 10, 11, 12, 16, 18, 19, 20, 24, 26, 27, 28, 32, 34, 35, 36, 40, 42, 43, 44, 48, 50, 51, 52, 56, 58, 59, 60, 64, 66, 67, 68, 72, 74, 75, 76, 80, 82, 83, 84, 88, 90, 91, 92, 96, 98, 99, 100, 104, 106, 107, 108, 112, 114, 115, 116, 120, 122, 123

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^2*(2+x+x^2+4*x^3)/((1-x)^2*(1+x)*(1+x^2)). - Colin Barker, May 13 2012

a(n) = (-11-(-1)^n-(2-i)*(-i)^n-(2+i)*i^n+8*n)/4 where i=sqrt(-1). - Colin Barker, May 14 2012

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

a(2k) = A047463(k), a(2k-1) = A047470(k). - Wesley Ivan Hurt, May 31 2016

E.g.f.: (8 + sin(x) - 2*cos(x) + (4*x - 5)*sinh(x) + (4*x - 6)*cosh(x))/2. - Ilya Gutkovskiy, May 31 2016

Sum_{n>=2} (-1)^n/a(n) = (2-sqrt(2))*Pi/16 + log(2)/8 + sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 21 2021

Maple

A047456:=n->(-11-(-1)^n-(2-I)*(-I)^n-(2+I)*I^n+8*n)/4: seq(A047456(n), n=1..100); # Wesley Ivan Hurt, May 31 2016

Mathematica

Select[Range[0, 300], MemberQ[{0, 2, 3, 4}, Mod[#, 8]]&] (* Vincenzo Librandi, May 16 2012 *)

Prog

(Magma) I:=[0, 2, 3, 4, 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

Crossrefs

Cf. A047463, A047470.

Sequence in context: A082224 A030478 A118252 * A279000 A073465 A174816

Adjacent sequences: A047453 A047454 A047455 * A047457 A047458 A047459

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved