|
| |
|
|
A100334
|
|
An inverse Catalan transform of F(2n).
|
|
6
|
|
|
|
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;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
LINKS
|
Table of n, a(n) for n=0..45.
Index entries for linear recurrences with constant coefficients, signature (3,-4,2,-1).
|
|
|
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, May 13 2008
a(n)=Sum_{k, 0<=k<=n} A109466(n,k)*A001906(k). [From Philippe Deléham, Oct 30 2008]
|
|
|
MATHEMATICA
|
Table[FullSimplify[GoldenRatio^n*Sqrt[2/5 + 2*Sqrt[5]/25]*Sin[Pi*n/5 + Pi/5] - (1/GoldenRatio)^n*Sqrt[2/5 - 2*Sqrt[5]/25]*Sin[2*Pi*n/5 + 2*Pi/5]], {n, 0, 41}] (* Arkadiusz Wesolowski, Oct 26 2012 *)
|
|
|
CROSSREFS
|
Sequence in context: A222128 A088972 A168505 * A254749 A129936 A253180
Adjacent sequences: A100331 A100332 A100333 * A100335 A100336 A100337
|
|
|
KEYWORD
|
easy,sign
|
|
|
AUTHOR
|
Paul Barry, Nov 17 2004
|
|
|
STATUS
|
approved
|
| |
|
|
