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

Author

Creighton Dement, Jun 11 2007

Keywords

• easy
• sign

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).

Crossrefs

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

Programs

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 *)

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]