

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


FORMULA

G.f.: x^3*(x+2)/(1x^2)^2.
a(n)=floor((n1)/2) + (n is odd)*floor((n1)/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..n1})  _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



