A175896
Number of lattice paths from (0,0) to (n,n) using steps S={(k,0),(0,k),(1,1)|0
Original entry on oeis.org
1, 2, 9, 57, 396, 2948, 23016, 185838, 1539066, 13001677, 111600446, 970550862, 8533427593, 75728797781, 677427655798, 6102015206945, 55299451023428, 503847366381836, 4612663920303329, 42409513650507927, 391425863599784588
Offset: 0
A175912
Number of lattice paths from (0,0) to (n,n) using steps S={(k,0),(0,k),(1,1)|k>0} which never go above the line y=x.
Original entry on oeis.org
1, 2, 9, 57, 411, 3181, 25803, 216486, 1863139, 16356925, 145914573, 1318844414, 12051758083, 111159508991, 1033505202643, 9675905948106, 91140492185703, 863107104436546, 8212873185281571, 78484928498979435, 752928813642151089
Offset: 0
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- J. P. S. Kung and A. de Mier, Catalan lattice paths with rook, bishop and spider steps, Journal of Combinatorial Theory, Series A 120 (2013) 379-389. - From _N. J. A. Sloane_, Dec 27 2012
- Joseph P. S. Kung, Anna de Mier, Rook and queen paths with boundaries, arXiv:1109.1806.
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Flatten[{1,RecurrenceTable[{(n+1)*a[n]-10*(n+2)*a[n+1]+(34*n+96)*a[n+2]-6*(8*n+29)*a[n+3]+5*(5*n+23)*a[n+4]-2*(n+6)*a[n+5]==0, a[1]==2, a[2]==9, a[3]==57, a[4]==411, a[5]==3181},a,{n,20}]}] (* Vaclav Kotesovec, Sep 07 2012 *)
A175900
Number of lattice paths from (0,0) to (n,n) using steps S={(k,0),(0,k),(1,1)|0
Original entry on oeis.org
1, 2, 9, 57, 411, 3150, 25274, 209719, 1784909, 15495058, 136672624, 1221370092, 11034687854, 100623850938, 924917387599, 8560734224711, 79717622732369, 746322905220237, 7020573752016609, 66324819580927731, 629004053328092981
Offset: 0
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