This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A220466 a((2*n-1)*2^p) = 4^p*(n-1) + 2^(p-1)*(1+2^p) , p >= 0 and n >= 1. 40
 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, 14, 58, 15, 31, 16, 528, 17, 35, 18, 74, 19, 39, 20, 164, 21, 43, 22, 90, 23, 47, 24, 392, 25, 51, 26, 106, 27, 55, 28, 228, 29, 59, 30, 122, 31, 63, 32, 2080, 33, 67, 34, 138, 35 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The a(n) appeared in the analysis of A220002, a sequence related to the Catalan numbers. 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. The cross references lead to sequences that have the same internal structure as this sequence. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Stephan Ralf, Some divide-and-conquer sequences with simple ordinary generating functions, The OEIS, Jan 01 2004. FORMULA 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). a(n) = ((n+1)/2)*(A060818(n)/A060818(n-1)) 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)) Recurrence: a(2n) = 4a(n) - 2^A007814(n), a(2n+1) = n+1. - Ralf Stephan, Dec 17 2013 MAPLE # First Maple program a := n -> 2^padic[ordp](n, 2)*(n+1)/2 : seq(a(n), n=1..69); # [Peter Luschny, Dec 24 2012] # Second Maple program 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); # Third Maple program 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); MATHEMATICA 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 *) PROG (PARI) a(n)=if(n%2, n\2+1, 4*a(n/2)-2^valuation(n/2, 2)) \\ Ralf Stephan, Dec 17 2013 (Haskell) Following Ralph Stephan's recurrence: import Data.List (transpose) a220466 n = a006519_list !! (n-1) a220466_list = 1 : concat    (transpose [zipWith (-) (map (* 4) a220466_list) a006519_list, [2..]]) -- Reinhard Zumkeller, Aug 31 2014 CROSSREFS 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) Sequence in context: A135515 A114486 A176743 * A090780 A184174 A277821 Adjacent sequences:  A220463 A220464 A220465 * A220467 A220468 A220469 KEYWORD nonn,easy,look AUTHOR Johannes W. Meijer, Dec 24 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 19 08:44 EDT 2019. Contains 322241 sequences. (Running on oeis4.)