A061171 One half of second column of Lucas bisection triangle (odd part).

3, 19, 79, 283, 940, 2982, 9171, 27581, 81557, 237995, 687158, 1966764, 5588259, 15780103, 44323195, 123920827, 345062176, 957403026, 2647935987, 7302634865, 20087869313, 55128445259, 150971982314

Offset

0,1

Comments

Numerator of g.f. is on half of row polynomial Sum_{m=0..2} A061187(1,m) * x^m.

Links

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).

Formula

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

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A000032, A000045, A001906, A002878, A005248.

Sequence in context: A093734 A099421 A241885 * A293561 A240286 A163431

Adjacent sequences: A061168 A061169 A061170 * A061172 A061173 A061174

Keyword

nonn,easy

Author

Wolfdieter Lang, Apr 20 2001

Status

approved