A047385 Numbers that are congruent to {2, 5} mod 7.
2, 5, 9, 12, 16, 19, 23, 26, 30, 33, 37, 40, 44, 47, 51, 54, 58, 61, 65, 68, 72, 75, 79, 82, 86, 89, 93, 96, 100, 103, 107, 110, 114, 117, 121, 124, 128, 131, 135, 138, 142, 145, 149, 152, 156, 159, 163, 166, 170
Offset: 1
Links
- David Lovler, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
Programs
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Maple
A047385:=n->4*n-2-floor(n/2); seq(A047385(k),k=1..100); # Wesley Ivan Hurt, Oct 16 2013
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Mathematica
Table[4 n - 2 - Floor[n/2], {n,100}] (* Wesley Ivan Hurt, Oct 16 2013 *) #+{2,5}&/@(7*Range[0,30])//Flatten (* Harvey P. Dale, Jul 15 2017 *) -
PARI
a(n)=(14*n-6)>>2 \\ Charles R Greathouse IV, Dec 05 2011
Formula
G.f.: x*(2 + 3*x + 2*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Dec 05 2011
a(n) = (14*n - (-1)^n - 7)/4. - Bruno Berselli, Dec 05 2011
a(n) = 4*n - 2 - floor(n/2). - Wesley Ivan Hurt, Oct 16 2013
E.g.f.: 2 + ((14*x - 7)*exp(x) - exp(-x))/4. - David Lovler, Sep 01 2022
From Amiram Eldar, Sep 26 2022: (Start)
a(n) = A113804(n)/2.
Sum_{n>=1} (-1)^(n+1)/a(n) = tan(3*Pi/14)*Pi/7. (End)
From Amiram Eldar, Nov 22 2024: (Start)
Product_{n>=1} (1 - (-1)^n/a(n)) = 2*sin(3*Pi/14) (A255249).
Product_{n>=1} (1 + (-1)^n/a(n)) = 1/(2*cos(Pi/7)) (A255240). (End)
Comments