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Search: id:A029578
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| A029578 |
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An obvious mixture of two sequences. |
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+0
9
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| 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; listen)
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OFFSET
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0,4
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COMMENT
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a(n) = number of ordered, length two, compositions of n with at least one odd summand - Len Smiley (smiley(AT)math.uaa.alaska.edu), Nov 25 2001
Also number of 0's in n-th row of triangle in A071037. - Hans Havermann (pxp(AT)rogers.com), May 26 2002
a(n) = (n - n mod 2)/(2 - n mod 2). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Jul 30 2002
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FORMULA
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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 (pbarry(AT)wit.ie), 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 (pbarry(AT)wit.ie), Jan 06 2005
a(n)=sum{k=0..n-2, gcd(n-k-1, k+1)} - Paul Barry (pbarry(AT)wit.ie), May 03 2005
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PROGRAM
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(PARI) a(n)=if(n%2, n-1, n/2)
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CROSSREFS
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Cf. A065423 (at least one even summand).
Cf. A009531.
Sequence in context: A126080 A060681 A060766 this_sequence A054345 A060367 A062968
Adjacent sequences: A029575 A029576 A029577 this_sequence A029579 A029580 A029581
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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