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 A159348 Transform of the finite sequence (1, 0, -1, 0, 1) by the T_{0,0} transform (see link). 3
 1, 1, 1, 4, 11, 24, 55, 128, 298, 693, 1611, 3745, 8706, 20239, 47050, 109378, 254273, 591113, 1374171, 3194560, 7426451, 17264404, 40134870, 93302253, 216901423, 504234633, 1172203306, 2725042075, 6334954246, 14726981894, 34236079265 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS G. C. Greubel, Table of n, a(n) for n = 0..2500 Richard Choulet, Curtz-like transformation. Index entries for linear recurrences with constant coefficients, signature (3,-2,1). FORMULA O.g.f.: f(z) = ((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2+z^4). EXAMPLE a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) for n>=7, with a(0)=1, a(1)=1, a(2)=1, a(3)=4, a(4)=11, a(5)=24, a(6)=55. MAPLE a(0):=1: a(1):=1:a(2):=1: a(3):=4:a(4):=11:a(5):=24:a(6):=55:for n from 4 to 31 do a(n+3):=3*a(n+2)-2*a(n+1)+a(n):od:seq(a(i), i=0..31); MATHEMATICA Join[{1, 1, 1, 4}, LinearRecurrence[{3, -2, 1}, {11, 24, 55}, 40]] (* or *) CoefficientList[Series[(-1+2 x-2 x^3+2 x^5-x^6)/(-1+3 x-2 x^2+x^3), {x, 0, 45}], x](* Harvey P. Dale, Oct 04 2011 *) PROG (PARI) m=50; v=concat([11, 24, 55], vector(m-3)); for(n=4, m, v[n]= 3*v[n-1] -2*v[n-2] +v[n-3]); concat([1, 1, 1, 4], v) \\ G. C. Greubel, Jun 16 2018 (MAGMA) I:=[11, 24, 55]; [1, 1, 1, 4] cat [n le 3 select I[n] else 3*Self(n-1) - 2*Self(n-2) +Self(n-3): n in [1..30]]; // G. C. Greubel, Jun 16 2018 CROSSREFS Cf. A137531, A159347. Sequence in context: A258472 A007678 A159350 * A159349 A192597 A181946 Adjacent sequences:  A159345 A159346 A159347 * A159349 A159350 A159351 KEYWORD nonn AUTHOR Richard Choulet, Apr 11 2009 STATUS approved

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Last modified February 27 03:50 EST 2020. Contains 332299 sequences. (Running on oeis4.)