A090692 Expansion of 2*(x^2-9*x+15) / ((1+x)*(1-3*x+x^2)).

30, 42, 146, 346, 942, 2430, 6398, 16714, 43794, 114618, 300110, 785662, 2056926, 5385066, 14098322, 36909850, 96631278, 252983934, 662320574, 1733977738, 4539612690, 11884860282, 31114968206, 81460044286, 213265164702, 558335449770, 1461741184658, 3826888104154

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,2,-1).

Formula

a(0)=30, a(1)=42, a(2)=146, a(n) = 2*a(n-1)+2*a(n-2)-a(n-3). - Harvey P. Dale, Aug 21 2014

a(n) = (2^(1-n)*(25*(-2)^n+(25-11*sqrt(5))*(3-sqrt(5))^n+(3+sqrt(5))^n*(25+11*sqrt(5))))/5. - Colin Barker, Oct 01 2016

Mathematica

CoefficientList[Series[2(x^2-9x+15)/(x^3-2x^2-2x+1), {x, 0, 30}], x] (* or *) LinearRecurrence[{2, 2, -1}, {30, 42, 146}, 30] (* Harvey P. Dale, Aug 21 2014 *)

Prog

(PARI) a(n) = round((2^(1-n)*(25*(-2)^n+(25-11*sqrt(5))*(3-sqrt(5))^n+(3+sqrt(5))^n*(25+11*sqrt(5))))/5) \\ Colin Barker, Oct 01 2016
(PARI) Vec(2*(x^2-9*x+15)/((1+x)*(1-3*x+x^2)) + O(x^40)) \\ Colin Barker, Oct 01 2016

Crossrefs

Sequence in context: A050776 A268697 A258358 * A196677 A225326 A226727

Adjacent sequences: A090689 A090690 A090691 * A090693 A090694 A090695

Keyword

nonn,easy

Author

Creighton Dement, Jan 08 2005

Status

approved