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A033190 Sum(binomial(n,k)*binomial(fibonacci(k)+1,2),k=0..n). 2
0, 1, 3, 9, 28, 90, 297, 1001, 3431, 11917, 41820, 147918, 526309, 1881009, 6744843, 24244145, 87300092, 314765506, 1135980801, 4102551897, 14823628015, 53581222773, 193724727804, 700551945014 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of (s(0), s(1), ..., s(2n)) such that 0 < s(i) < 10 and |s(i) - s(i-1)| = 1 for i = 1,2,....,2n, s(0) = 1, s(2n) = 3. - Herbert Kociemba, Jun 14 2004

LINKS

Table of n, a(n) for n=0..23.

Index entries for linear recurrences with constant coefficients, signature (8,-21,20,-5).

FORMULA

G.f.: (-x^4+6x^3-5x^2+x)/[(1-3x+x^2)(1-5x+5x^2)].

a(n)=(1/5)*Sum(r, 1, 9, Sin(r*Pi/10)Sin(3*r*Pi/10)(2Cos(r*Pi/10))^(2n)), n>=1 a(n)=8a(n-1)-21a(n-2)+20a(n-3)-5a(n-4), n>=5. - Herbert Kociemba, Jun 14 2004

MAPLE

A033190 := proc(n)

    add(binomial(n, k)*binomial(combinat[fibonacci](k)+1, 2), k=0..n) ;

end proc: # R. J. Mathar, Feb 18 2016

CROSSREFS

Sequence in context: A094164 A094803 A094826 * A071724 A000245 A143739

Adjacent sequences:  A033187 A033188 A033189 * A033191 A033192 A033193

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 20 20:12 EST 2018. Contains 299385 sequences. (Running on oeis4.)