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A191649 Number of lattice paths from (0,0) to (n,n) using steps (0,1), (1,0), (1,1), (2,2). 1

%I

%S 1,3,14,71,379,2082,11651,66051,378064,2180037,12644861,73695358,

%T 431209313,2531556197,14904832196,87970766447,520337606401,

%U 3083584244460,18304476242735,108820740004749,647817646760368,3861215365595659,23039691494489015,137615812845579390

%N Number of lattice paths from (0,0) to (n,n) using steps (0,1), (1,0), (1,1), (2,2).

%H G. C. Greubel, <a href="/A191649/b191649.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: 1/sqrt(x^4 +2*x^3 -x^2 -6*x +1). - _Mark van Hoeij_, Apr 17 2013

%F D-finite with recurrence: n*a(n) +3*(-2*n+1)*a(n-1) +(-n+1)*a(n-2) +(2*n-3)*a(n-3) +(n-2)*a(n-4)=0. - _R. J. Mathar_, Oct 08 2016

%t CoefficientList[Series[1/Sqrt[x^4 + 2 x^3 - x^2 - 6 x + 1], {x, 0, 23}], x] (* _Michael De Vlieger_, Oct 08 2016 *)

%o (PARI) /* same as in A092566 but use */

%o steps=[[0,1], [1,0], [1,1], [2,2]];

%o /* _Joerg Arndt_, Jun 30 2011 */

%o (PARI) my(x='x+O('x^30)); Vec(1/sqrt(x^4+2*x^3-x^2-6*x+1)) \\ _G. C. Greubel_, Apr 29 2019

%o (MAGMA) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 1/Sqrt(x^4+2*x^3-x^2-6*x+1) )); // _G. C. Greubel_, Apr 29 2019

%o (Sage) (1/sqrt(x^4+2*x^3-x^2-6*x+1)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 29 2019

%Y Cf. A001850, A026641, A036355, A137644, A192364, A192365, A192369, A191354.

%K nonn

%O 0,2

%A _Joerg Arndt_, Jun 30 2011

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Last modified February 19 19:06 EST 2020. Contains 332047 sequences. (Running on oeis4.)