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A131039 Expansion of (1-x)*(2*x^2-4*x+1)/(1-2*x+5*x^2-4*x^3+x^4). 3
1, -3, -5, 7, 26, 0, -97, -97, 265, 627, -362, -2702, -1351, 8733, 13775, -18817, -70226, 0, 262087, 262087, -716035, -1694157, 978122, 7300802, 3650401, -23596563, -37220045, 50843527, 189750626, 0, -708158977, -708158977, 1934726305, 4577611587, -2642885282, -19726764302, -9863382151 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Unsigned bisection gives match to A002316 (Related to Bernoulli numbers). Note that all numbers in A002316 appear to be in A002531 (Numerators of continued fraction convergents to sqrt(3)) as well. a(12*n+5) = (0,0,0,0,...)

LINKS

Robert Israel, Table of n, a(n) for n = 0..3492

Index entries for linear recurrences with constant coefficients, signature (2, -5, 4, -1).

FORMULA

a(0)=1, a(1)=-3, a(2)=-5, a(3)=7, a(n)=2*a(n-1)-5*a(n-2)+4*a(n-3)-a(n-4) [From Harvey P. Dale, Aug 31 2011]

MAPLE

f:= gfun:-rectoproc({a(0)=1, a(1)=-3, a(2)=-5, a(3)=7, a(n)=2*a(n-1)-5*a(n-2)+4*a(n-3)-a(n-4)}, a(n), remember):

map(f, [$0..100]); # Robert Israel, Dec 25 2016

MATHEMATICA

CoefficientList[Series[(1-x)(2x^2-4x+1)/(1-2x+5x^2-4x^3+x^4), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, -5, 4, -1}, {1, -3, -5, 7}, 50] (* Harvey P. Dale, Aug 31 2011 *)

PROG

Floretion Algebra Multiplication Program, FAMP Code: 2tesseq['i + .5i' + .5j' + .5k' + .5e]

CROSSREFS

Cf. A131040, A131041, A131042, A002316, A002531.

Sequence in context: A045966 A146148 A098475 * A249544 A027449 A126670

Adjacent sequences:  A131036 A131037 A131038 * A131040 A131041 A131042

KEYWORD

easy,sign

AUTHOR

Creighton Dement, Jun 11 2007

STATUS

approved

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Last modified November 22 06:11 EST 2017. Contains 295076 sequences.