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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).
1
1, 2, 10, 46, 233, 1196, 6274, 33292, 178378, 962616, 5224965, 28494124, 156000816, 856903772, 4720235840, 26064910068, 144236627991, 799671246842, 4440913771641, 24699098156578, 137553727513369, 766990846033320, 4281404671954689, 23923170440346544
OFFSET
0,2
LINKS
FORMULA
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
MAPLE
P := (4*x^6-13*x^4-18*x^3+41*x^2+22*x-5)*A^3+(4-3*x^2)*A+1;
series(RootOf(P, A), x=0, 30); # Mark van Hoeij, Apr 17 2013
# second Maple program:
b:= proc(p) b(p):= `if`(p=[0$2], 1, `if`(min(p[])<0, 0,
add(b(p-l), l=[[0, 1], [0, 2], [1, 0], [2, 2]])))
end:
a:= n-> b([n$2]):
seq(a(n), n=0..30); # Alois P. Heinz, Aug 18 2014
MATHEMATICA
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 *)
PROG
(PARI) /* same as in A092566 but use */
steps=[[0, 1], [0, 2], [1, 0], [2, 2]];
/* Joerg Arndt, Jun 30 2011 */
CROSSREFS
Sequence in context: A029706 A191644 A009640 * A081167 A321274 A166107
KEYWORD
nonn
AUTHOR
Joerg Arndt, Jun 30 2011
STATUS
approved