A131039 Expansion of (1-x)*(2*x^2-4*x+1)/(1-2*x+5*x^2-4*x^3+x^4).

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

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,...)

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

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) [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 *)

Crossrefs

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

Sequence in context: A045966 A146148 A098475 * A362684 A294924 A249544

Adjacent sequences: A131036 A131037 A131038 * A131040 A131041 A131042

Keyword

easy,sign

Author

Creighton Dement, Jun 11 2007

Status

approved