The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A029578 The natural numbers interleaved with the even numbers. 21
 0, 0, 1, 2, 2, 4, 3, 6, 4, 8, 5, 10, 6, 12, 7, 14, 8, 16, 9, 18, 10, 20, 11, 22, 12, 24, 13, 26, 14, 28, 15, 30, 16, 32, 17, 34, 18, 36, 19, 38, 20, 40, 21, 42, 22, 44, 23, 46, 24, 48, 25, 50, 26, 52, 27, 54, 28, 56, 29, 58, 30, 60, 31, 62, 32, 64, 33, 66, 34, 68, 35, 70, 36, 72 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS a(n) = number of ordered, length two, compositions of n with at least one odd summand - Len Smiley, Nov 25 2001 Also number of 0's in n-th row of triangle in A071037. - Hans Havermann, May 26 2002 a(n) = (n - n mod 2)/(2 - n mod 2). - Reinhard Zumkeller, Jul 30 2002 For n > 2: a(n) = number of odd terms in row n-2 of triangle A265705. - Reinhard Zumkeller, Dec 15 2015 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1). FORMULA a(n) = (3*n/2-1+(1-n/2)*(-1)^n)/2. a(n+4)=2*a(n+2)-a(n). G.f.: x^2*(2x+1)/(1-x^2)^2; a(n)=floor((n+1)/2)+(n is odd)*floor((n+1)/2) a(n) = floor(n/2)*binomial(2, mod(n, 2)) - Paul Barry, May 25 2003 a(2*n) = n, a(2*n-1) = 2*n-2. a(-n)=-A065423(n+2). a(n) = Sum_{k=0..floor((n-2)/2)} (C(n-k-2, k) mod 2)((1+(-1)^k)/2)*2^A000120(n-2k-2). - Paul Barry, Jan 06 2005 a(n) = Sum_{k=0..n-2} gcd(n-k-1, k+1). - Paul Barry, May 03 2005 For n>6: a(n) = floor(a(n-1)*a(n-2)/a(n-3)). [Reinhard Zumkeller, Mar 06 2011] MATHEMATICA With[{nn=40}, Riffle[Range[0, nn], Range[0, 2nn, 2]]] (* or *) LinearRecurrence[ {0, 2, 0, -1}, {0, 0, 1, 2}, 80] (* Harvey P. Dale, Aug 23 2015 *) PROG (PARI) a(n)=if(n%2, n-1, n/2) (Haskell) import Data.List (transpose) a029578 n =  (n - n `mod` 2) `div` (2 - n `mod` 2) a029578_list = concat \$ transpose [a001477_list, a005843_list] -- Reinhard Zumkeller, Nov 27 2012 CROSSREFS Cf. A065423 (at least one even summand). Cf. A009531. Cf. A001477, A005843, A211538 (partial sums). Cf. A265705. Sequence in context: A343327 A060766 A321015 * A054345 A352956 A304214 Adjacent sequences:  A029575 A029576 A029577 * A029579 A029580 A029581 KEYWORD nonn,easy AUTHOR EXTENSIONS Explicated definition by Reinhard Zumkeller, Nov 27 2012 Title simplified by Sean A. Irvine, Feb 29 2020 STATUS approved

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

Last modified October 7 07:33 EDT 2022. Contains 357270 sequences. (Running on oeis4.)