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Search: id:A057681
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| A057681 |
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Sum((-1)^j*binomial(n,3*j),j=0..floor(n/3)). |
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+0
4
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| 1, 1, 1, 0, -3, -9, -18, -27, -27, 0, 81, 243, 486, 729, 729, 0, -2187, -6561, -13122, -19683, -19683, 0, 59049, 177147, 354294, 531441, 531441, 0, -1594323, -4782969, -9565938, -14348907, -14348907, 0, 43046721, 129140163, 258280326, 387420489, 387420489
(list; graph; listen)
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OFFSET
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0,5
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LINKS
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Ira Gessel, The Smith College diploma problem.
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FORMULA
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G.f.: (1-x)^2/((1-x)^3+x^3); a(n)=0^n/3+2*3^((n-2)/2)cos(pi*n/6). - Paul Barry (pbarry(AT)wit.ie), Feb 26 2004
Binomial transform of (1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, ...) E.g.f. : 2exp(3x/2)cos(sqrt(3)x/2)/3+1/3; a(n)=(((3+sqrt(-3))/2)^n+((3-sqrt(-3))/2)^n)/3+0^n/3. - Paul Barry (pbarry(AT)wit.ie), Feb 27 2004
a(n)=6a(n-1)-15a(n-2)+20a(n-3)-15a(n-4)+6a(n-5). - Paul Curtz (bpcrtz(AT)free.fr), Jan 02 2008
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MAPLE
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A057681 := n->add((-1)^j*binomial(n, 3*j), j=0..floor(n/3));
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CROSSREFS
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Cf. A009116.
Cf. A009545.
Sequence in context: A112559 A030784 A123877 this_sequence A103312 A159794 A100967
Adjacent sequences: A057678 A057679 A057680 this_sequence A057682 A057683 A057684
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KEYWORD
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sign
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Oct 20 2000
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