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 A220466 #32 Apr 29 2020 07:42:46
%S A220466 1,3,2,10,3,7,4,36,5,11,6,26,7,15,8,136,9,19,10,42,11,23,12,100,13,27,
%T A220466 14,58,15,31,16,528,17,35,18,74,19,39,20,164,21,43,22,90,23,47,24,392,
%U A220466 25,51,26,106,27,55,28,228,29,59,30,122,31,63,32,2080,33,67,34,138,35
%N A220466 a((2*n-1)*2^p) = 4^p*(n-1) + 2^(p-1)*(1+2^p), p >= 0 and n >= 1.
%C A220466 The a(n) appeared in the analysis of A220002, a sequence related to the Catalan numbers.
%C A220466 The first Maple program makes use of a program by Peter Luschny for the calculation of the a(n) values. The second Maple program shows that this sequence has a beautiful internal structure, see the first formula, while the third Maple program makes optimal use of this internal structure for the fast calculation of a(n) values for large n.
%C A220466 The cross references lead to sequences that have the same internal structure as this sequence.
%H A220466 Reinhard Zumkeller, <a href="/A220466/b220466.txt">Table of n, a(n) for n = 1..10000</a>
%H A220466 Ralf Stephan, <a href="https://oeis.org/somedcgf.html">Some divide-and-conquer sequences with simple ordinary generating functions</a>, The OEIS, Jan 01 2004.
%F A220466 a((2*n-1)*2^p) = 4^p*(n-1) + 2^(p-1)*(1+2^p), p >= 0 and n >= 1. Observe that a(2^p) = A007582(p).
%F A220466 a(n) = ((n+1)/2)*(A060818(n)/A060818(n-1))
%F A220466 a(n) = (-1/64)*(q(n+1)/q(n))/(2*n+1) with q(n) = (-1)^(n+1)*2^(4*n-5)*(2*n)!*A060818(n-1) or q(n) = (1/8)*A220002(n-1)*1/(A098597(2*n-1)/A046161(2*n))*1/(A008991(n-1)/A008992(n-1))
%F A220466 Recurrence: a(2n) = 4a(n) - 2^A007814(n), a(2n+1) = n+1. - _Ralf Stephan_, Dec 17 2013
%p A220466 # First Maple program
%p A220466 a := n -> 2^padic[ordp](n, 2)*(n+1)/2 : seq(a(n), n=1..69); # _Peter Luschny_, Dec 24 2012
%p A220466 # Second Maple program
%p A220466 nmax:=69: for p from 0 to ceil(simplify(log[2](nmax))) do for n from 1 to ceil(nmax/(p+2)) do a((2*n-1)*2^p) := 4^p*(n-1) + 2^(p-1)*(1+2^p) od: od: seq(a(n), n=1..nmax);
%p A220466 # Third Maple program
%p A220466 nmax:=69: for p from 0 to ceil(simplify(log[2](nmax))) do n:=2^p: n1:=1: while n <= nmax do a(n) := 4^p*(n1-1)+2^(p-1)*(1+2^p): n:=n+2^(p+1): n1:= n1+1: od: od: seq(a(n), n=1..nmax);
%t A220466 A220466 = Module[{n, p}, p = IntegerExponent[#, 2]; n = (#/2^p + 1)/2; 4^p*(n - 1) + 2^(p - 1)*(1 + 2^p)] &; Array[A220466, 50] (* _JungHwan Min_, Aug 22 2016 *)
%o A220466 (PARI) a(n)=if(n%2,n\2+1,4*a(n/2)-2^valuation(n/2,2)) \\ _Ralf Stephan_, Dec 17 2013
%o A220466 (Haskell) -- Following Ralf Stephan's recurrence:
%o A220466 import Data.List (transpose)
%o A220466 a220466 n = a006519_list !! (n-1)
%o A220466 a220466_list = 1 : concat
%o A220466 (transpose [zipWith (-) (map (* 4) a220466_list) a006519_list, [2..]])
%o A220466 -- _Reinhard Zumkeller_, Aug 31 2014
%Y A220466 Cf. A000027 (the natural numbers), A000120 (1's-counting sequence), A000265 (remove 2's from n), A001316 (Gould's sequence), A001511 (the ruler function), A003484 (Hurwitz-Radon numbers), A003602 (a fractal sequence), A006519 (highest power of 2 dividing n), A007814 (binary carry sequence), A010060 (Thue-Morse sequence), A014577 (dragon curve), A014707 (dragon curve), A025480 (nim-values), A026741, A035263 (first Feigenbaum symbolic sequence), A037227, A038712, A048460, A048896, A051176, A053381 (smooth nowhere-zero vector fields), A055975 (Gray code related), A059134, A060789, A060819, A065916, A082392, A085296, A086799, A088837, A089265, A090739, A091512, A091519, A096268, A100892, A103391, A105321 (a fractal sequence), A109168 (a continued fraction), A117973, A129760, A151930, A153733, A160467, A162728, A181988, A182241, A191488 (a companion to Gould's sequence), A193365, A220466 (this sequence).
%K A220466 nonn,easy,look
%O A220466 1,2
%A A220466 _Johannes W. Meijer_, Dec 24 2012