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A191684 Number of lattice paths from (0,0) to (n,n) using steps (0,1), (0,2), (1,0), (2,2).

%I A191684 #17 May 27 2015 10:34:06
%S A191684 1,2,10,46,233,1196,6274,33292,178378,962616,5224965,28494124,
%T A191684 156000816,856903772,4720235840,26064910068,144236627991,799671246842,
%U A191684 4440913771641,24699098156578,137553727513369,766990846033320,4281404671954689,23923170440346544
%N A191684 Number of lattice paths from (0,0) to (n,n) using steps (0,1), (0,2), (1,0), (2,2).
%H A191684 Alois P. Heinz, <a href="/A191684/b191684.txt">Table of n, a(n) for n = 0..1000</a>
%F A191684 G.f.: A(x) where (4*x^6-13*x^4-18*x^3+41*x^2+22*x-5)*A(x)^3+(4-3*x^2)*A(x)+1=0. - _Mark van Hoeij_, Apr 17 2013
%p A191684 P := (4*x^6-13*x^4-18*x^3+41*x^2+22*x-5)*A^3+(4-3*x^2)*A+1;
%p A191684 series(RootOf(P,A),x=0,30); # _Mark van Hoeij_, Apr 17 2013
%p A191684 # second Maple program:
%p A191684 b:= proc(p) b(p):= `if`(p=[0$2], 1, `if`(min(p[])<0, 0,
%p A191684       add(b(p-l), l=[[0, 1], [0, 2], [1, 0], [2, 2]])))
%p A191684     end:
%p A191684 a:= n-> b([n$2]):
%p A191684 seq(a(n), n=0..30);  # _Alois P. Heinz_, Aug 18 2014
%t A191684 b[p_List] := b[p] = If[p == {0, 0}, 1, If[Min[p] < 0, 0, Sum[b[p-l], {l, {{0, 1}, {0, 2}, {1, 0}, {2, 2}}}]]]; a[n_] := b[{n, n}]; Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, May 27 2015, after _Alois P. Heinz_ *)
%o A191684 (PARI) /* same as in A092566 but use */
%o A191684 steps=[[0,1], [0,2], [1,0], [2,2]];
%o A191684 /* _Joerg Arndt_, Jun 30 2011 */
%K A191684 nonn
%O A191684 0,2
%A A191684 _Joerg Arndt_, Jun 30 2011