A164037 Expansion of (5-9*x)/(1-6*x+7*x^2).

5, 21, 91, 399, 1757, 7749, 34195, 150927, 666197, 2940693, 12980779, 57299823, 252933485, 1116502149, 4928478499, 21755355951, 96032786213, 423909225621, 1871225850235, 8259990522063, 36461362180733, 160948239429957

Offset

0,1

Comments

Binomial transform of A161941 without initial 2. Third binomial transform of A164095. Inverse binomial transform of A161731 without initial 1.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..100 from Vincenzo Librandi)

Index entries for linear recurrences with constant coefficients, signature (6,-7).

Formula

a(n) = 6*a(n-1)-7*a(n-2) for n > 1; a(0) = 5, a(1) = 21.

G.f.: (5-9*x)/(1-6*x+7*x^2).

a(n) = ((5+3*sqrt(2))*(3+sqrt(2))^n+(5-3*sqrt(2))*(3-sqrt(2))^n)/2.

E.g.f.: (5*cosh(sqrt(2)*x) + 3*sqrt(2)*sinh(sqrt(2)*x))*exp(3*x). - G. C. Greubel, Sep 08 2017

Mathematica

CoefficientList[Series[(5-9x)/(1-6x+7x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{6, -7}, {5, 21}, 30] (* Harvey P. Dale, Apr 27 2017 *)

Prog

(Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((5+3*r)*(3+r)^n+(5-3*r)*(3-r)^n)/2: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 10 2009
(PARI) Vec((5-9*x)/(1-6*x+7*x^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Crossrefs

Cf. A161941, A164095 (5, 6, 10, 12, 20, 24, ...), A161731.

Sequence in context: A188707 A360580 A333538 * A218961 A168444 A125784

Adjacent sequences: A164034 A164035 A164036 * A164038 A164039 A164040

Keyword

nonn,easy

Author

Al Hakanson (hawkuu(AT)gmail.com), Aug 08 2009

Extensions

Edited and extended beyond a(5) by Klaus Brockhaus, Aug 10 2009

Status

approved