A047473 Numbers that are congruent to {2, 3} mod 8.
2, 3, 10, 11, 18, 19, 26, 27, 34, 35, 42, 43, 50, 51, 58, 59, 66, 67, 74, 75, 82, 83, 90, 91, 98, 99, 106, 107, 114, 115, 122, 123, 130, 131, 138, 139, 146, 147, 154, 155, 162, 163, 170, 171, 178, 179, 186, 187, 194, 195, 202, 203, 210, 211, 218, 219, 226, 227, 234
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
Programs
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Mathematica
Flatten[# + {2,3} &/@ (8 Range[0, 30])] (* or *) LinearRecurrence[{1, 1, -1}, {2, 3, 10}, 60] (* Harvey P. Dale, Sep 28 2012 *)
Formula
a(n) = 8*n - a(n-1) - 11 for n>1, a(1)=2. - Vincenzo Librandi, Aug 06 2010
From R. J. Mathar, Oct 08 2011: (Start)
a(n) = 4*n - 7/2 - 3*(-1)^n/2.
G.f.: x*(2 + x + 5*x^2)/((1 + x)*(1 - x)^2). (End)
a(1)=2, a(2)=3, a(3)=10; for n>3, a(n) = a(n-1) + a(n-2) - a(n-3). - Harvey P. Dale, Sep 28 2012
Sum_{n>=1} (-1)^(n+1)/a(n) = (2-sqrt(2))*Pi/16 + sqrt(2)*log(sqrt(2)+1)/8 - log(2)/8. - Amiram Eldar, Dec 18 2021
Extensions
More terms from Vincenzo Librandi, Aug 06 2010
Comments