A047398 Numbers that are congruent to {3, 6} mod 8.
3, 6, 11, 14, 19, 22, 27, 30, 35, 38, 43, 46, 51, 54, 59, 62, 67, 70, 75, 78, 83, 86, 91, 94, 99, 102, 107, 110, 115, 118, 123, 126, 131, 134, 139, 142, 147, 150, 155, 158, 163, 166, 171, 174, 179, 182, 187, 190, 195, 198, 203, 206, 211, 214, 219, 222, 227, 230
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
Crossrefs
Programs
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Maple
A047398:=n->4*n-(3+(-1)^n)/2: seq(A047398(n), n=1..100); # Wesley Ivan Hurt, Jan 30 2017
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Mathematica
Flatten[# + {3, 6} & /@ (8 Range[0, 28])] (* Arkadiusz Wesolowski, Sep 25 2012 *) LinearRecurrence[{1,1,-1},{3,6,11},60] (* Harvey P. Dale, Oct 26 2020 *) -
Maxima
makelist(4*n + mod(n, 2) - 2, n, 1, 100); /* Franck Maminirina Ramaharo, Aug 06 2018 */
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Python
def A047398(n): return ((n<<2)|(n&1))-2 # Chai Wah Wu, Mar 30 2024
Formula
a(n) = 8*n - a(n-1) - 7, n > 1. - Vincenzo Librandi, Aug 05 2010
From R. J. Mathar, Dec 05 2011: (Start)
a(n) = 4*n - (3 + (-1)^n)/2.
G.f.: x*(3+3*x+2*x^2) / ( (1+x)*(x-1)^2 ). (End)
From Franck Maminirina Ramaharo, Aug 06 2018: (Start)
a(n) = a(n-1) + a(n-2) - a(n-3), n > 3.
a(n) = 4*n + (n mod 2) - 2.
a(n) = A047470(n) + 3.
a(2*n) = A017137(n-1).
a(2*n-1) = A017101(n-1).
E.g.f.: ((8*x - 3)*exp(x) - exp(-x) + 4)/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 18 2021