A010700 - OEIS

%I #32 Oct 13 2025 00:00:00

%S 2,10,2,10,2,10,2,10,2,10,2,10,2,10,2,10,2,10,2,10,2,10,2,10,2,10,2,

%T 10,2,10,2,10,2,10,2,10,2,10,2,10,2,10,2,10,2,10,2,10,2,10,2,10,2,10,

%U 2,10,2,10,2,10,2,10,2,10,2,10,2,10,2,10,2,10

%N Period 2: repeat (2,10).

%C Continued fraction expansion of A176057. - _R. J. Mathar_, Mar 08 2012

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).

%F a(n) = -4*(-1)^n + 6. _Paolo P. Lava_, Oct 20 2006

%F G.f.: 2*(1+5*x)/((1-x)*(1+x)). - _R. J. Mathar_, Nov 21 2011

%F a(n) = 3^(1 - (-1)^n) + 1. - _Bruno Berselli_, Dec 29 2015

%F a(n) = 2 + 8*(n mod 2) = 2 + 8*A000035(n). - _M. F. Hasler_, Feb 27 2020

%F From _Elmo R. Oliveira_, Oct 12 2025: (Start)

%F E.g.f.: 2*cosh(x) + 10*sinh(x).

%F a(n) = 2*A010686(n). (End)

%p A010700 := n -> 2 + irem(n,2)*8; # _M. F. Hasler_, Feb 27 2020

%t PadRight[{}, 100, {2, 10}] (* _M. F. Hasler_, Feb 27 2020 *)

%o (PARI) a(n)=2+n%2*8 \\ _Charles R Greathouse IV_, Dec 21 2011

%o (PARI) apply( {A010700(n)=2+bittest(n,0)<<3}, [0..99]) \\ _M. F. Hasler_, Feb 27 2020

%o (Magma) &cat [[2,10]^^35]; // _Bruno Berselli_, Dec 29 2015

%Y Cf. A010679 (3^(1-(-1)^n) - 1), A010686, A176057.

%Y Equals 2 + A010679 = 2 + 8*A000035.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_