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A146962 a(n) = 10*a(n-1) - 19*a(n-2) with a(0)=1, a(1)=5. 2
1, 5, 31, 215, 1561, 11525, 85591, 636935, 4743121, 35329445, 263175151, 1960492055, 14604592681, 108796577765, 810478516711, 6037650189575, 44977410078241, 335058747180485, 2496016680318271, 18594050606753495 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A143648.

Inverse binomial transform of A145301.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (10,-19).

FORMULA

a(n) = ((5 + sqrt(6))^n + (5 - sqrt(6))^n)/2.

G.f.: (1-5*x)/(1-10*x+19*x^2). - Philippe Deléham and Klaus Brockhaus, Nov 05 2008

a(n) = (Sum_{k=0..n} A098158(n,k)*5^(2*k)*6^(n-k))/5^n. - Philippe Deléham, Nov 06 2008

E.g.f.: exp(5*x)*cosh(sqrt(6)*x). - G. C. Greubel, Jan 08 2020

MAPLE

seq(coeff(series((1-5*x)/(1-10*x+19*x^2), x, n+1), x, n), n = 0..30); # G. C. Greubel, Jan 08 2020

MATHEMATICA

LinearRecurrence[{10, -19}, {1, 5}, 30] (* Harvey P. Dale, Apr 27 2014 *)

CoefficientList[Series[(1-5x)/(1-10x+19x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Apr 28 2014 *)

PROG

(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r6>:=NumberField(x^2-6); S:=[ ((5+r6)^n+(5-r6)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 05 2008

(PARI) my(x='x+O('x^30)); Vec((1-5*x)/(1-10*x+19*x^2)) \\ G. C. Greubel, Jan 08 2020

(Sage)

def A146962_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P( (1-5*x)/(1-10*x+19*x^2) ).list()

A146962_list(30) # G. C. Greubel, Jan 08 2020

(GAP) a:=[1, 5];; for n in [3..30] do a[n]:=10*a[n-1]-19*a[n-2]; od; a; # G. C. Greubel, Jan 08 2020

CROSSREFS

Cf. A098158, A143648, A145301.

Sequence in context: A104091 A153292 A087457 * A269730 A036758 A153232

Adjacent sequences:  A146959 A146960 A146961 * A146963 A146964 A146965

KEYWORD

nonn,easy

AUTHOR

Al Hakanson (hawkuu(AT)gmail.com), Nov 03 2008

EXTENSIONS

Extended beyond a(7) by Klaus Brockhaus, Nov 05 2008

Edited by Klaus Brockhaus, Jul 15 2009

Name from Philippe Deléham and Klaus Brockhaus, Nov 05 2008

STATUS

approved

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Last modified July 15 15:04 EDT 2020. Contains 335772 sequences. (Running on oeis4.)