A047535 Numbers that are congruent to {4, 7} mod 8.
4, 7, 12, 15, 20, 23, 28, 31, 36, 39, 44, 47, 52, 55, 60, 63, 68, 71, 76, 79, 84, 87, 92, 95, 100, 103, 108, 111, 116, 119, 124, 127, 132, 135, 140, 143, 148, 151, 156, 159, 164, 167, 172, 175, 180, 183, 188, 191, 196, 199, 204, 207, 212, 215, 220, 223, 228, 231
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
Programs
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Maple
A047535:=n->4*n - (1 + (-1)^n)/2; seq(A047535(n), n=1..100); # Wesley Ivan Hurt, Feb 24 2014
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Mathematica
Table[4n - (1 + (-1)^n)/2, {n, 100}] (* Wesley Ivan Hurt, Feb 24 2014 *) -
Maxima
makelist(4*n - (1 + (-1)^n)/2, n, 1, 100); /* Franck Maminirina Ramaharo, Jul 22 2018 */
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Python
def A047535(n): return (n<<2)-(n&1^1) # Chai Wah Wu, Mar 30 2024
Formula
a(n) = 8*n - a(n-1) - 5 (with a(1)=4). - Vincenzo Librandi, Aug 06 2010
a(n) = 4*n -(1 + (-1)^n)/2. - Arkadiusz Wesolowski, Sep 18 2012
G.f.: x*(4+3*x+x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Jul 10 2015
From Franck Maminirina Ramaharo, Jul 22 2018: (Start)
a(n) = A047470(n) + 4.
E.g.f.: (2 - exp(-x) + (8*x - 1)*exp(x))/2. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)+1)*Pi/16 - log(2)/4 - sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 11 2021
Comments