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A029578 An obvious mixture of two sequences: the natural numbers interleaved with the even numbers. 18
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 two-way infinite sequences

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: A202479 A161660 A060766 * A054345 A060367 A267451

Adjacent sequences:  A029575 A029576 A029577 * A029579 A029580 A029581

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Explicated definition by Reinhard Zumkeller, Nov 27 2012

STATUS

approved

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Last modified September 25 18:05 EDT 2017. Contains 292499 sequences.