A141722 - OEIS

%I #28 Apr 25 2024 09:26:52

%S 1,25,121,505,2041,8185,32761,131065,524281,2097145,8388601,33554425,

%T 134217721,536870905,2147483641,8589934585,34359738361,137438953465,

%U 549755813881,2199023255545,8796093022201,35184372088825,140737488355321,562949953421305

%N a(n) = 8*4^n - 7.

%H G. C. Greubel, <a href="/A141722/b141722.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..200 from Vincenzo Librandi)

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4).

%F a(n) = 4*a(n-1) + 21.

%F G.f.: (1+20*x)/((1-x)*(1-4*x)). - _R. J. Mathar_, Sep 13 2008

%F a(n) = 10*A000975(2n) + A000975(2n+1). - _Paul Curtz_, Sep 17 2008

%F From _G. C. Greubel_, Sep 30 2017: (Start)

%F a(n) = 5*a(n-1) - 4*a(n-2).

%F E.g.f.: 8*exp(4*x) - 7*exp(x). (End)

%p A141722:=n->8*4^n-7; seq(A141722(n), n=0..30); # _Wesley Ivan Hurt_, Feb 15 2014

%t Table[8*4^n-7, {n, 0, 30}] (* _Wesley Ivan Hurt_, Feb 15 2014 *)

%o (Magma) [8*4^n-7: n in [0..30]]; // _Vincenzo Librandi_, May 31 2011

%o (PARI) x='x+O('x^50); Vec((1+20*x)/((1-x)*(1-4*x))) \\ _G. C. Greubel_, Sep 30 2017

%Y Cf. A000975.

%K nonn,easy

%O 0,2

%A _Paul Curtz_, Sep 12 2008

%E Edited by _N. J. A. Sloane_, Sep 13 2008

%E More terms from _R. J. Mathar_, Sep 13 2008

%E More terms from _Vincenzo Librandi_, May 31 2011

%E Better name (using formula from _R. J. Mathar_) from _Joerg Arndt_, Feb 16 2014