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A061171
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One half of second column of Lucas bisection triangle (odd part).
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6
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3, 19, 79, 283, 940, 2982, 9171, 27581, 81557, 237995, 687158, 1966764, 5588259, 15780103, 44323195, 123920827, 345062176, 957403026, 2647935987, 7302634865, 20087869313, 55128445259, 150971982314
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OFFSET
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0,1
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COMMENTS
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Numerator of g.f. is on half of row polynomial Sum_{m=0..2} A061187(1,m) * x^m.
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
É. Czabarka, R. Flórez, L. Junes, A Discrete Convolution on the Generalized Hosoya Triangle, Journal of Integer Sequences, 18 (2015), #15.1.6.
Index entries for linear recurrences with constant coefficients, signature (6,-11,6,-1).
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FORMULA
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2*a(n) = A060924(n+1, 1).
G.f.: (1+x)*(3-2*x)/(1-3*x+x^2)^2.
a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4), with a(0)=3, a(1)=19, a(2)=79, a(3)=283. - Harvey P. Dale, Oct 11 2012
a(n) = Fibonacci(2*n+4) + n*Lucas(2*n+3). - Lechoslaw Ratajczak, May 06 2020
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MATHEMATICA
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CoefficientList[Series[(1+x)(3-2x)/(1-3x+x^2)^2, {x, 0, 30}], x] (* or *) LinearRecurrence[{6, -11, 6, -1}, {3, 19, 79, 283}, 30] (* Harvey P. Dale, Oct 11 2012 *)
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PROG
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(PARI) my(x='x+O('x^30)); Vec((1+x)*(3-2*x)/(1-3*x+x^2)^2) \\ G. C. Greubel, Dec 21 2017
(MAGMA) I:=[3, 19, 79, 283]; [n le 4 select I[n] else 6*Self(n-1) - 11*Self(n-2) + 6*Self(n-3) - Self(n-4): n in [1..30]]; // G. C. Greubel, Dec 21 2017
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CROSSREFS
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Cf. A000032, A000045, A001906, A002878, A005248.
Sequence in context: A093734 A099421 A241885 * A293561 A240286 A163431
Adjacent sequences: A061168 A061169 A061170 * A061172 A061173 A061174
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang, Apr 20 2001
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STATUS
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approved
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