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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A047463, A047470.

Programs

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

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 *)

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