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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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