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A027994 a(n) = (F(2n+3) - F(n))/2 where F() = Fibonacci numbers A000045. 6
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; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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, Jun 02 2004

Diagonal sums of triangle in A125171. - Philippe Deléham, Jan 14 2014

LINKS

Table of n, a(n) for n=0..27.

FORMULA

G.f.: (1-x)^2/((1-x-x^2)*(1-3*x+x^2)). - Floor van Lamoen and N. J. A. Sloane, Jan 21 2001

a(n) = Sum_{k=0..n} T(n, k)*T(n, n+k), T given by A027926.

a(n) = 2*a(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, Jan 21 2001

a(n) = (2/5)*Sum_{k=1..4} sin(2*Pi*k/5)*sin(3*Pi*k/5)*(1+2*cos(Pi*k/5))^(n+1)). - Herbert Kociemba, Jun 02 2004

a(-1-2n) = A056014(2n), a(-2n) = A005207(2n-1).

PROG

(PARI) a(n)=(fibonacci(2*n+3)-fibonacci(n))/2

CROSSREFS

Cf. A000667, A059216, A059219, A059502, A027926.

Sequence in context: A217661 A244399 A291142 * A319503 A295572 A027068

Adjacent sequences:  A027991 A027992 A027993 * A027995 A027996 A027997

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified August 14 18:32 EDT 2020. Contains 336483 sequences. (Running on oeis4.)