A047617 Numbers that are congruent to {2, 5} mod 8.
2, 5, 10, 13, 18, 21, 26, 29, 34, 37, 42, 45, 50, 53, 58, 61, 66, 69, 74, 77, 82, 85, 90, 93, 98, 101, 106, 109, 114, 117, 122, 125, 130, 133, 138, 141, 146, 149, 154, 157, 162, 165, 170, 173, 178, 181, 186, 189, 194, 197, 202, 205, 210, 213, 218, 221, 226, 229, 234
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
Programs
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Mathematica
Select[Range[300],MemberQ[{2,5},Mod[#,8]]&] (* or *) LinearRecurrence[ {1,1,-1},{2,5,10},80] (* Harvey P. Dale, Feb 23 2016 *) -
Maxima
makelist(4*n -(5 + (-1)^n)/2, n, 1, 100); /* Franck Maminirina Ramaharo, Jul 22 2018 */
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Python
def A047617(n): return (n-1<<2)+1+(n&1) # Chai Wah Wu, Mar 30 2024
Formula
a(n) = 8*n - a(n-1) - 9 (with a(1)=2). - Vincenzo Librandi, Aug 06 2010
a(n) = 4*n - (5 + (-1)^n)/2. - Arkadiusz Wesolowski, Sep 18 2012
G.f.: (2+3*x+3*x^2)/((-1+x)^2*(1+x)). - Harvey P. Dale, Feb 23 2016
a(1)=2, a(2)=5, a(3)=10, a(n) = a(n-1) + a(n-2) - a(n-3). - Harvey P. Dale, Feb 23 2016
From Franck Maminirina Ramaharo, Jul 22 2018: (Start)
a(n) = A047470(n) + 2.
E.g.f.: (6 - exp(-x) + (8*x - 5)*exp(x))/2. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(2)*Pi/16 - log(2)/8 + sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 11 2021
Extensions
More terms from Vincenzo Librandi, Aug 06 2010
Comments