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A100334
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An inverse Catalan transform of F(2n).
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6
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0, 1, 2, 2, 0, -5, -13, -21, -21, 0, 55, 144, 233, 233, 0, -610, -1597, -2584, -2584, 0, 6765, 17711, 28657, 28657, 0, -75025, -196418, -317811, -317811, 0, 832040, 2178309, 3524578, 3524578, 0, -9227465, -24157817, -39088169, -39088169, 0, 102334155, 267914296, 433494437, 433494437, 0, -1134903170
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| G.f.: x(1-x)/(1-3x+4x^2-2x^3+x^4); a(n)=(phi)^n*sqrt(2/5+2sqrt(5)/25)sin(pi*(n+1)/5) -(1/phi)^n*sqrt(2/5-2sqrt(5)/25)sin(2pi*(n+1)/5), where phi=(1+sqrt(5))/2; a(n)=sum{k=0..floor(n/2), C(n-k, k)(-1)^k*sum{j=0..n-k, C(n-k, j)F(j)}}; a(n)=sum{k=0..floor(n/2), C(n-k, k)(-1)^k*F(2n-2k)}.
a(n)=3a(n-1)-4a(n-2)+2a(n-3)-a(n-4). - Paul Curtz (bpcrtz(AT)free.fr), May 13 2008
a(n)=Sum_{k, 0<=k<=n} A109466(n,k)*A001906(k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 30 2008]
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CROSSREFS
| Sequence in context: A166299 A088972 A168505 * A129936 A157077 A185896
Adjacent sequences: A100331 A100332 A100333 * A100335 A100336 A100337
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KEYWORD
| easy,sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Nov 17 2004
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