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 A144864 #64 Apr 19 2024 02:28:26
%S A144864 1,21,341,5461,87381,1398101,22369621,357913941,5726623061,
%T A144864 91625968981,1466015503701,23456248059221,375299968947541,
%U A144864 6004799503160661,96076792050570581,1537228672809129301,24595658764946068821,393530540239137101141,6296488643826193618261,100743818301219097892181
%N A144864 a(n) = (4*16^(n-1)-1)/3.
%C A144864 Old name was: A144863, read as binary numbers, converted to base 10.
%C A144864 All numbers in this sequence for n>1 are congruent to 5 mod 16. - _Artur Jasinski_, Sep 25 2008
%C A144864 From _Omar E. Pol_, Sep 10 2011: (Start)
%C A144864 It appears that this is a bisection of A002450.
%C A144864 It appears that this is a bisection of A084241.
%C A144864 It appears that this is a bisection of A153497.
%C A144864 It appears that this is a bisection of A088556, if n>=2.
%C A144864 (End)
%C A144864 All of the above is trivially true. - _Joerg Arndt_, Aug 19 2014
%C A144864 The aerated sequence (b(n))n>=1 = [1, 0, 21, 0, 341, 0, 5461, 0, 87381, ...] is a fourth-order linear divisibility sequence; that is, a(n) divides a(m) whenever n divides m. It is the case P1 = 0, P2 = -9, Q = -4 of the 3-parameter family of 4th-order linear divisibility sequences found by Williams and Guy. - _Peter Bala_, Aug 26 2022
%H A144864 Vincenzo Librandi, <a href="/A144864/b144864.txt">Table of n, a(n) for n = 1..500</a>
%H A144864 H. C. Williams and R. K. Guy, <a href="http://dx.doi.org/10.1142/S1793042111004587">Some fourth-order linear divisibility sequences</a>, Intl. J. Number Theory 7 (5) (2011) 1255-1277.
%H A144864 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (17,-16).
%F A144864 a(n) = 16^n/12 - 1/3; a(n) = 16*a(n-1) + 5, a(1)=1. - _Artur Jasinski_, Sep 25 2008
%F A144864 G.f.: x*(1+4*x) / ( (16*x-1)*(x-1) ). - _R. J. Mathar_, Jan 06 2011
%F A144864 a(n)=b such that Integral_{x=-Pi/2..Pi/2} (-1)^(n+1)*2^(2*n-3)*(cos((2*n-1)*x))/(5/4+sin(x)) dx = c+b*log(3). - _Francesco Daddi_, Aug 02 2011
%F A144864 a(n) = (2^(4*n-2)-1)/3. - _Klaus Purath_, Jan 31 2021
%F A144864 From _Jianing Song_, Aug 30 2022: (Start)
%F A144864 a(n) = A001045(4*n-2).
%F A144864 a(n+1) - a(n) = 10*A013776(n-1) = 20*A001025(n-1) for n >= 1.
%F A144864 a(n) = 10*A098704(n) + 1 = 20*A131865(n-2) + 1 for n >= 2. (End)
%F A144864 E.g.f.: (exp(16*x) - 4*exp(x) + 3)/12. - _Stefano Spezia_, Apr 18 2024
%t A144864 Table[1/3 (-1 + 16^(n - 1)) + 16^(n - 1), {n, 1, 17}] (* _Artur Jasinski_, Sep 25 2008 *)
%t A144864 LinearRecurrence[{17,-16},{1,21},20] (* _Harvey P. Dale_, Jun 29 2022 *)
%o A144864 (Magma) [16^n/12-1/3: n in [1..20]]; // _Vincenzo Librandi_, Aug 03 2011
%o A144864 (PARI) vector(66,n,(4*16^(n-1)-1)/3) \\ _Joerg Arndt_, Aug 19 2014
%Y A144864 Cf. A001025, A002450, A013776, A056830, A084241, A088556, A094028, A098704, A131865, A135576, A144863, A153497.
%Y A144864 Third quadrisection of Jacobsthal numbers A001045; the other quadrisections are A195156 (first), A139792 (second), and A141060 (fourth).
%K A144864 easy,nonn
%O A144864 1,2
%A A144864 _Artur Jasinski_, Sep 23 2008
%E A144864 New name from _Joerg Arndt_, Aug 19 2014