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A065423
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Number of ordered length 2 compositions of n with at least one even summand.
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6
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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; internal format)
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OFFSET
| 1,3
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LINKS
| Index entries for two-way infinite sequences
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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 (pbarry(AT)wit.ie), May 02 2005
a(n)= Sum( (-1)^i (floor(i/2) + mod(i + 1, 2) ), {i = 1..n-1}) - Olivier GERARD (olivier.gerard(AT)gmail.com), Jun 21 2007
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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
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PROG
| (PARI) a(n)=n-=2; if(n%2, n+1, n/2)
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CROSSREFS
| Cf. A097140 (first differences), A030451 (absolute first differences).
Sequence in context: A130107 A107130 A194747 * A008733 A154280 A004795
Adjacent sequences: A065420 A065421 A065422 * A065424 A065425 A065426
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KEYWORD
| nonn
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AUTHOR
| Len Smiley (smiley(AT)math.uaa.alaska.edu), Nov 23 2001
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