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A192417 Number of lattice paths from (0,0) to (n,n) using steps (0,1), (1,0), (2,2), (3,3).

%I A192417 #22 Sep 08 2022 08:45:57
%S A192417 1,2,7,27,107,436,1810,7609,32288,138009,593311,2562725,11112720,
%T A192417 48347332,210936119,922550622,4043488129,17755735241,78099099877,
%U A192417 344033901804,1517535718392,6701979806379,29630948706756,131136723532257,580901892464599,2575423975663301
%N A192417 Number of lattice paths from (0,0) to (n,n) using steps (0,1), (1,0), (2,2), (3,3).
%H A192417 G. C. Greubel, <a href="/A192417/b192417.txt">Table of n, a(n) for n = 0..1000</a>
%F A192417 G.f.: 1/sqrt(x^6+2*x^5+x^4-2*x^3-2*x^2-4*x+1). - _Mark van Hoeij_, Apr 17 2013
%F A192417 D-finite with recurrence: n*a(n) +2*(-2*n+1)*a(n-1) +2*(-n+1)*a(n-2) +(-2*n+3)*a(n-3) +(n-2)*a(n-4) +(2*n-5)*a(n-5) +(n-3)*a(n-6)=0. - _R. J. Mathar_, Oct 08 2016
%t A192417 CoefficientList[Series[1/Sqrt[x^6+2x^5+x^4-2x^3-2x^2-4x+1], {x, 0, 25}], x] (* _Michael De Vlieger_, Oct 08 2016 *)
%o A192417 (PARI) /* same as in A092566 but use */
%o A192417 steps=[[0,1], [1,0], [2,2], [3,3]];
%o A192417 /* _Joerg Arndt_, Jun 30 2011 */
%o A192417 (PARI) my(x='x+O('x^30)); Vec(1/sqrt(x^6+2*x^5+x^4-2*x^3-2*x^2-4*x+1)) \\ _G. C. Greubel_, Apr 29 2019
%o A192417 (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 1/Sqrt(x^6+2*x^5+x^4-2*x^3-2*x^2-4*x+1) )); // _G. C. Greubel_, Apr 29 2019
%o A192417 (Sage) (1/sqrt(x^6+2*x^5+x^4-2*x^3-2*x^2-4*x+1)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 29 2019
%Y A192417 Cf. A001850, A026641, A036355, A137644, A192364, A192365, A192369, A191354.
%K A192417 nonn
%O A192417 0,2
%A A192417 _Joerg Arndt_, Jun 30 2011