|
Search: id:A027994
|
|
| |
|
| 1, 2, 6, 16, 43, 114, 301, 792, 2080, 5456, 14301, 37468, 98137, 256998, 672946, 1761984, 4613239, 12078110, 31621701, 82787980, 216743836, 567446112, 1485598681, 3889356696, 10182482353, 26658108074, 69791870526, 182717549872
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Substituting x(1-x)/(1-2x) into x^2/(1-x^2) yields x^2*g.f. of sequence.
The number of (s(0), s(1), ..., s(n+1)) such that 0 < s(i) < 5 and |s(i) - s(i-1)| <= 1 for i = 1,2,....,n+1, s(0) = 2, s(n+1) = 3. - Herbert Kociemba (kociemba(AT)t-online.de), Jun 02 2004
|
|
FORMULA
|
G.f.: (1-x)^2/((1-x-x^2)*(1-3*x+x^2)) - Floor van Lamoen (fvlamoen(AT)hotmail.com) and njas, Jan 21 2001
a(n)=(2/5)*Sum(k, 1, 4, Sin(2Pi*k/5)Sin(3Pi*k/5)(1+2Cos(Pi*k/5))^(n+1)) - Herbert Kociemba (kociemba(AT)t-online.de), Jun 02 2004
|
|
PROGRAM
|
(PARI) a(n)=(fibonacci(2*n+3)-fibonacci(n))/2
|
|
CROSSREFS
|
a(n)=Sum{T(n,k)*T(n,n+k)}, 0<=k<=n, T given by A027926.
a(n) = 2a(n-1) + Sum{m<n-1}a(m) + F(n-1) = A059512(n+2) - F(n) where F(n) is the n-th Fibonacci number (A000045) - Floor van Lamoen (fvlamoen(AT)hotmail.com), Jan 21 2001
Cf. A000667, A059216, A059219, A059502, A027926.
a(-1-2n)=A056014(2n), a(-2n)=A005207(2n-1).
Sequence in context: A111282 A115730 A003142 this_sequence A027068 A118041 A105073
Adjacent sequences: A027991 A027992 A027993 this_sequence A027995 A027996 A027997
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Clark Kimberling (ck6(AT)evansville.edu)
|
|
|
Search completed in 0.002 seconds
|
