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 A192368 Number of lattice paths from (0,0) to (n,n) using steps (1,0), (2,0), (0,2), (1,1). 3
 1, 1, 6, 19, 94, 396, 1870, 8541, 40284, 189274, 899260, 4281168, 20487156, 98299384, 473118174, 2282322211, 11034087438, 53443135944, 259283934816, 1259795078566, 6129223177272, 29856164309124, 145592506783224, 710686739172096, 3472285996766556, 16979257639328076 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA G.f. -16*(3*s+1)*s^(3/2)/(3*s^4+2*s^3-76*s^2+6*s+1) where s satisfies 16*x*(3*s+1)*s+(s^2-18*s+1)*(s-1) = 0. - Mark van Hoeij, Apr 16 2013 MAPLE s := RootOf( 16*x*(3*s+1)*s+(s^2-18*s+1)*(s-1), s): ogf := -16*(3*s+1)*s^(3/2)/(3*s^4+2*s^3-76*s^2+6*s+1): series(ogf, x=0, 20); # Mark van Hoeij, Apr 16 2013 # second Maple program: b:= proc(x, y) option remember;       `if`(min(x, y)<0, 0, `if`(max(x, y)=0, 1,        b(x-1, y)+b(x-2, y)+b(x, y-2)+b(x-1, y-1)))     end: a:= n-> b(n\$2): seq(a(n), n=0..35);  # Alois P. Heinz, May 16 2017 MATHEMATICA a[0, 0] = 1; a[n_, k_] /; n >= 0 && k >= 0 := a[n, k] = a[n, k - 1] + a[n, k - 2] + a[n - 1, k - 1] + a[n - 2, k]; a[_, _] = 0; a[n_] := a[n, n]; a /@ Range[0, 25] (* Jean-François Alcover, Oct 14 2019 *) PROG (PARI) /* same as in A092566 but use */ steps=[[1, 0], [2, 0], [0, 2], [1, 1]]; /* Joerg Arndt, Jun 30 2011 */ CROSSREFS Cf. A001850, A026641, A036355, A137644, A192364, A192365, A192369. Sequence in context: A279512 A111510 A151277 * A323686 A285853 A138748 Adjacent sequences:  A192365 A192366 A192367 * A192369 A192370 A192371 KEYWORD nonn AUTHOR Joerg Arndt, Jul 01 2011 STATUS approved

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Last modified September 24 17:33 EDT 2021. Contains 347651 sequences. (Running on oeis4.)