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A190989 a(n) = 10*a(n-1) - 7*a(n-2), with a(0)=0, a(1)=1. 2
0, 1, 10, 93, 860, 7949, 73470, 679057, 6276280, 58009401, 536160050, 4955534693, 45802226580, 423333522949, 3912719643430, 36163861773657, 334249580232560, 3089348769910001, 28553740637472090, 263911964985350893, 2439243465391204300, 22545050899014586749 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (10,-7).

FORMULA

G.f.: x/ ( 1-10*x+7*x^2 ). - R. J. Mathar, May 26 2011

a(n) = (sqrt(2)/12)*((5+3*sqrt(2))^n - (5-3*sqrt(2))^n). - Paolo P. Lava, May 31 2011

E.g.f.: (1/(3*sqrt(2)))*exp(5*x)*sinh(3*sqrt(2)*x). - G. C. Greubel, Sep 16 2022

MATHEMATICA

LinearRecurrence[{10, -7}, {0, 1}, 50]

PROG

(Magma) [Round(7^((n-1)/2)*Evaluate(ChebyshevU(n), 5/Sqrt(7))): n in [0..30]]; // G. C. Greubel, Sep 15 2022

(SageMath)

A190989 = BinaryRecurrenceSequence(10, -7, 0, 1)

[A190989(n) for n in (0..30)] # G. C. Greubel, Sep 15 2022

CROSSREFS

Cf. A190958 (index to generalized Fibonacci sequences)

Sequence in context: A265242 A262173 A103944 * A224696 A099295 A167589

Adjacent sequences: A190986 A190987 A190988 * A190990 A190991 A190992

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, May 24 2011

STATUS

approved

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Last modified January 29 23:01 EST 2023. Contains 359939 sequences. (Running on oeis4.)