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A065423 Number of ordered length 2 compositions of n with at least one even summand. 9
0, 0, 2, 1, 4, 2, 6, 3, 8, 4, 10, 5, 12, 6, 14, 7, 16, 8, 18, 9, 20, 10, 22, 11, 24, 12, 26, 13, 28, 14, 30, 15, 32, 16, 34, 17, 36, 18, 38, 19, 40, 20, 42, 21, 44, 22, 46, 23, 48, 24, 50, 25, 52, 26, 54, 27, 56, 28, 58, 29, 60, 30, 62, 31, 64, 32, 66, 33, 68, 34, 70, 35, 72, 36, 74 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

(Fourth column of table A210530)/2 for n>2. - Boris Putievskiy, Jan 29 2013

LINKS

Table of n, a(n) for n=1..75.

Index entries for two-way infinite sequences

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

FORMULA

G.f.: x^3*(x+2)/(1-x^2)^2.

a(n)=floor((n-1)/2) + (n is odd)*floor((n-1)/2)

a(n+2)=sum{k=0..n, gcd(n, k) mod 2}; - Paul Barry, May 02 2005

a(n)= Sum( (-1)^i (floor(i/2) + mod(i + 1, 2) ), {i = 1..n-1}) - _Olivier Gérard_, Jun 21 2007

a(n) = (3*n+2-(n+2)*(-1)^n)/4, n > 1. - Boris Putievskiy, Jan 29 2013

a(n) = A026741(n)-1. - Wesley Ivan Hurt, Jun 23 2013

EXAMPLE

a(7) = 6 because we can write 7 = 1+6 = 2+5 = 3+4 = 4+3 = 5+2 = 6+1; a(8) = 3 because we can write 8 = 2+6 = 4+4 = 6+2.

MATHEMATICA

LinearRecurrence[{0, 2, 0, -1}, {0, 0, 2, 1}, 100] (* Harvey P. Dale, May 14 2014 *)

PROG

(PARI) a(n)=n-=2; if(n%2, n+1, n/2)

CROSSREFS

Cf. A097140 (first differences), A030451 (absolute first differences), A210530.

Sequence in context: A130107 A107130 A194747 * A239242 A008733 A244515

Adjacent sequences:  A065420 A065421 A065422 * A065424 A065425 A065426

KEYWORD

nonn,easy

AUTHOR

Len Smiley, Nov 23 2001

STATUS

approved

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Last modified February 17 12:32 EST 2020. Contains 331996 sequences. (Running on oeis4.)