%I #26 Mar 17 2024 02:10:41
%S 3,43,683,10923,174763,2796203,44739243,715827883,11453246123,
%T 183251937963,2932031007403,46912496118443,750599937895083,
%U 12009599006321323,192153584101141163,3074457345618258603,49191317529892137643
%N Fourth quadrisection of Jacobsthal numbers A001045: a(n)=16a(n-1)-5.
%C Jacobsthal numbers ending with the decimal digit 3. - _Jianing Song_, Aug 30 2022
%H Vincenzo Librandi, <a href="/A141060/b141060.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (17,-16).
%F a(n) = A139792(n) + A013776(n).
%F a(n+1) - a(n) = 10*A013709(n) = 40*A001025(n).
%F G.f.: (3-8*x)/((1-x)*(1-16*x)). [_Colin Barker_, Apr 05 2012]
%F a(0)=3, a(1)=43, a(n)=17*a(n-1)-16*a(n-2). - _Harvey P. Dale_, Mar 16 2015
%F From _Jianing Song_, Aug 30 2022: (Start)
%F a(n) = A001045(4*n+3).
%F a(n) = 10*A141032(n) + 3 = 20*A098704(n+1) + 1 = 40*A131865(n-1) + 1 for n >= 1. (End)
%t LinearRecurrence[{17,-16},{3,43},30] (* _Harvey P. Dale_, Mar 16 2015 *)
%o (Magma) [(1/3)*(1+8*16^n): n in [0..25]]; // _Vincenzo Librandi_, May 25 2011
%o (PARI) a(n)=8*16^n\3+1 \\ _Charles R Greathouse IV_, May 25, 2011
%Y The other quadrisections of A001045 are A195156 (first), A139792 (second), and A144864 (third).
%K nonn,easy,less
%O 0,1
%A _Paul Curtz_, Jul 30 2008