This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A195156 #52 Dec 17 2022 12:43:36
%S A195156 0,5,85,1365,21845,349525,5592405,89478485,1431655765,22906492245,
%T A195156 366503875925,5864062014805,93824992236885,1501199875790165,
%U A195156 24019198012642645,384307168202282325,6148914691236517205,98382635059784275285,1574122160956548404565
%N A195156 a(n) = (16^n-1)/3.
%C A195156 Numbers of A002450 that are multiples of 5. Also sequence found by reading the line from 0, in the direction 0, 5,..., in the square spiral whose edges are the Jacobsthal numbers A001045 and whose vertices are the numbers A000975. This is a semi-diagonal in the spiral.
%C A195156 In binary, these numbers are 101...01 (see A031982). - _Alonso del Arte_, May 20 2017
%C A195156 0 together with Jacobsthal numbers ending with the decimal digit 5. - _Jianing Song_, Aug 30 2022
%H A195156 Vincenzo Librandi, <a href="/A195156/b195156.txt">Table of n, a(n) for n = 0..800</a>
%H A195156 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (17,-16).
%F A195156 From _Bruno Berselli_, Sep 19 2011: (Start)
%F A195156 G.f.: 5*x/((1-x)*(1-16*x)).
%F A195156 a(n) = A002450(2n) = (16^n-1)/3.
%F A195156 a(n) = 5*A131865(n-1) = a(n-1) + 5*A001025(n-1) = 16*a(n-1) + 5 for n > 0. (End)
%F A195156 From _Jianing Song_, Aug 30 2022: (Start)
%F A195156 a(n) = A001045(4*n).
%F A195156 a(n+1) - a(n) = 10*A013777(n-1) = 80*A001025(n-1) for n >= 1. (End)
%F A195156 E.g.f.: exp(x)*(exp(15*x) - 1)/3. - _Stefano Spezia_, Dec 17 2022
%p A195156 A195156:=n->(16^n-1)/3; seq(A195156(k), k=0..50); # _Wesley Ivan Hurt_, Oct 24 2013
%t A195156 Table[(16^n - 1)/3, {n, 0, 63}] (* _Wesley Ivan Hurt_, Oct 24 2013 *)
%o A195156 (Magma) [(16^n-1)/3:n in [0..20]]; // _Vincenzo Librandi_, Sep 20 2011
%o A195156 (PARI) for(n=0,50, print1((16^n - 1)/3, ", ")) \\ _G. C. Greubel_, Oct 11 2017
%Y A195156 Bisection of A002450.
%Y A195156 Cf. A000975, A001025, A013777, A031982, A131865.
%Y A195156 First quadrisection of Jacobsthal numbers A001045; the other quadrisections are A139792 (second), A144864 (third), and A141060 (fourth).
%K A195156 nonn,easy
%O A195156 0,2
%A A195156 _Omar E. Pol_, Sep 10 2011
%E A195156 New sequence name suggested by _Charles R Greathouse IV_ using Berselli's formula. - Sep 19 2011