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A049664 a(n)=(F(6n+3)-2)/32, where F=A000045 (the Fibonacci sequence). 8
0, 1, 19, 342, 6138, 110143, 1976437, 35465724, 636406596, 11419853005, 204920947495, 3677157201906, 65983908686814, 1184033199160747, 21246613676206633, 381255012972558648, 6841343619829849032, 122762930143964723929, 2202891398971535181691 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Partial sums of Chebyshev polynomials S(n,18).

LINKS

Table of n, a(n) for n=0..18.

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (19,-19,1).

FORMULA

G.f.: x/(1-19*x+19*x^2-x^3) = x/((1-x)*(1-18*x+x^2).

a(n+1) = sum(S(k, 18), k=0..n) with n>=0, S(k, 18) = U(k, 9) = A049660(k+1).

a(n) = 19*a(n-1)-19*a(n-2)+a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=19.

a(n) = 18*a(n-1)-a(n-2)+1, n>=2, a(0)=0, a(1)=1.

a(n+1) = (S(n+1, 18)-S(n, 18) -1)/16, n>=0.

a(n) = -1/16-(1/80)*(9-4*sqrt(5))^n*sqrt(5)+(1/32)*(9-4*sqrt(5))^n+(1/80)*sqrt(5)*(9+4 *sqrt(5))^n+(1/32)*(9+4*sqrt(5))^n. - Paolo P. Lava, Oct 03 2008

a(n) = 1/8*sum(Fibonacci(6*k), k=0..n). - Gary Detlefs, Dec 07 2010

PROG

(PARI) a(n)=fibonacci(6*n+3)\32 \\ Charles R Greathouse IV, Oct 07 2016

CROSSREFS

Cf. A053606.

Cf. A212336 for more sequences with g.f. of the type 1/(1-k*x+k*x^2-x^3).

Sequence in context: A142549 A049629 A162805 * A163110 A163453 A163968

Adjacent sequences:  A049661 A049662 A049663 * A049665 A049666 A049667

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

EXTENSIONS

Chebyshev comments from Wolfdieter Lang, Aug 31 2004

STATUS

approved

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Last modified December 10 00:24 EST 2016. Contains 278993 sequences.