A047485 Numbers that are congruent to {0, 3, 5, 7} mod 8.
0, 3, 5, 7, 8, 11, 13, 15, 16, 19, 21, 23, 24, 27, 29, 31, 32, 35, 37, 39, 40, 43, 45, 47, 48, 51, 53, 55, 56, 59, 61, 63, 64, 67, 69, 71, 72, 75, 77, 79, 80, 83, 85, 87, 88, 91, 93, 95, 96, 99, 101, 103, 104, 107, 109, 111, 112, 115, 117, 119, 120, 123, 125
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
Programs
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Magma
[n : n in [0..150] | n mod 8 in [0, 3, 5, 7]]; // Wesley Ivan Hurt, Jun 04 2016
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Maple
A047485:=n->(-5+I^(2*n)-I*(-I)^n+I*I^n+8*n)/4: seq(A047485(n), n=1..100); # Wesley Ivan Hurt, Jun 04 2016
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Mathematica
Select[Range[0,120], MemberQ[{0,3,5,7}, Mod[#,8]]&] (* Harvey P. Dale, May 20 2011 *)
Formula
From Colin Barker, May 14 2012: (Start)
G.f.: x^2*(3+2*x+2*x^2+x^3)/((1-x)^2*(1+x)*(1+x^2)).
a(n) = (-5+(-1)^n-i*(-i)^n+i*i^n+8*n)/4 where i=sqrt(-1). (End)
From Wesley Ivan Hurt, Jun 04 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
E.g.f.: (2 - sin(x) + (4*x - 3)*sinh(x) + (4*x - 2)*cosh(x))/2. - Ilya Gutkovskiy, Jun 04 2016
Sum_{n>=2} (-1)^n/a(n) = (8-sqrt(2))*log(2)/16 + sqrt(2)*log(2+sqrt(2))/8 - (3-sqrt(2))*Pi/16. - Amiram Eldar, Dec 23 2021