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A047385 Numbers that are congruent to {2, 5} mod 7.

%I A047385 #43 Nov 22 2024 06:26:55
%S A047385 2,5,9,12,16,19,23,26,30,33,37,40,44,47,51,54,58,61,65,68,72,75,79,82,
%T A047385 86,89,93,96,100,103,107,110,114,117,121,124,128,131,135,138,142,145,
%U A047385 149,152,156,159,163,166,170
%N A047385 Numbers that are congruent to {2, 5} mod 7.
%C A047385 Also, numbers n such that (n^2+3)/7 is a nonnegative integer. - _Bruno Berselli_, Jan 16 2016
%H A047385 David Lovler, <a href="/A047385/b047385.txt">Table of n, a(n) for n = 1..1000</a>
%H A047385 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A047385 G.f.: x*(2 + 3*x + 2*x^2) / ( (1+x)*(x-1)^2 ). - _R. J. Mathar_, Dec 05 2011
%F A047385 a(n) = (14*n - (-1)^n - 7)/4. - _Bruno Berselli_, Dec 05 2011
%F A047385 a(n) = 4*n - 2 - floor(n/2). - _Wesley Ivan Hurt_, Oct 16 2013
%F A047385 E.g.f.: 2 + ((14*x - 7)*exp(x) - exp(-x))/4. - _David Lovler_, Sep 01 2022
%F A047385 From _Amiram Eldar_, Sep 26 2022: (Start)
%F A047385 a(n) = A113804(n)/2.
%F A047385 Sum_{n>=1} (-1)^(n+1)/a(n) = tan(3*Pi/14)*Pi/7. (End)
%F A047385 From _Amiram Eldar_, Nov 22 2024: (Start)
%F A047385 Product_{n>=1} (1 - (-1)^n/a(n)) = 2*sin(3*Pi/14) (A255249).
%F A047385 Product_{n>=1} (1 + (-1)^n/a(n)) = 1/(2*cos(Pi/7)) (A255240). (End)
%p A047385 A047385:=n->4*n-2-floor(n/2); seq(A047385(k),k=1..100); # _Wesley Ivan Hurt_, Oct 16 2013
%t A047385 Table[4 n - 2 - Floor[n/2], {n,100}] (* _Wesley Ivan Hurt_, Oct 16 2013 *)
%t A047385 #+{2,5}&/@(7*Range[0,30])//Flatten (* _Harvey P. Dale_, Jul 15 2017 *)
%o A047385 (PARI) a(n)=(14*n-6)>>2 \\ _Charles R Greathouse IV_, Dec 05 2011
%Y A047385 Cf. A113804, A255240, A255249.
%K A047385 nonn,easy
%O A047385 1,1
%A A047385 _N. J. A. Sloane_