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%I #47 Sep 01 2022 19:47:53
%S 0,3,7,10,14,17,21,24,28,31,35,38,42,45,49,52,56,59,63,66,70,73,77,80,
%T 84,87,91,94,98,101,105,108,112,115,119,122,126,129,133,136,140,143,
%U 147,150,154,157,161,164,168,171,175,178,182,185,189,192,196,199,203
%N Numbers that are congruent to {0, 3} mod 7.
%C Numbers k such that k^2/7 + k*(k + 1)/7 = k*(2*k + 1)/7 is a nonnegative integer. - _Bruno Berselli_, Feb 14 2017
%H David Lovler, <a href="/A047355/b047355.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F a(n) = a(n-2) + 7 = a(n-1) + a(n-2) - a(n-3). - _Henry Bottomley_, Jan 19 2001
%F From _Bruno Berselli_, Sep 12 2011: (Start)
%F G.f.: x^2*(3 + 4*x)/((1 + x)*(1 - x)^2).
%F a(n) = (14*n - (-1)^n - 15)/4. (End)
%F a(n+1) = Sum_{k>=0} A030308(n,k)*A125176(k+2). - _Philippe Deléham_, Oct 17 2011
%F a(n) = 2*n - 2 + floor((3*n - 3)/2). - _Wesley Ivan Hurt_, Jan 30 2014
%F E.g.f.: 4 + ((14*x - 15)*exp(x) - exp(-x))/4. - _David Lovler_, Aug 31 2022
%p A047355:=n->(14*n - (-1)^n - 15)/4; seq(A047355(n), n=1..100); # _Wesley Ivan Hurt_, Jan 30 2014
%t Table[(14n - (-1)^n - 15)/4, {n, 100}] (* _Wesley Ivan Hurt_, Jan 30 2014 *)
%o (Haskell)
%o a047355 n = a047355_list !! (n-1)
%o a047355_list = scanl (+) 0 a010702_list -- _Reinhard Zumkeller_, Jul 05 2012
%o (PARI) a(n)=n\2*7 - 4 + n%2*4 \\ _Charles R Greathouse IV_, Aug 01 2016
%Y Cf. A030123, A010702 (first differences).
%Y Cf. A030308, A125176.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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