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A047456
Numbers that are congruent to {0, 2, 3, 4} mod 8.
2
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
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
Sequence in context: A082224 A030478 A118252 * A279000 A073465 A174816
KEYWORD
nonn,easy
STATUS
approved