cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

Wolfdieter Lang, Apr 20 2001

Keywords

Comments

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

Crossrefs

Programs

  • 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
  • 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 *)
  • 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
    

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