A108786 Yet another version of the Catalan triangle A008315.

1, 1, 1, 1, 1, 2, 1, 3, 2, 1, 4, 5, 1, 5, 9, 5, 1, 6, 14, 14, 1, 7, 20, 28, 14, 1, 8, 27, 48, 42, 1, 9, 35, 75, 90, 42, 1, 10, 44, 110, 165, 132, 1, 11, 54, 154, 275, 297, 132, 1, 12, 65, 208, 429, 572, 429, 1, 13, 77, 273, 637, 1001, 1001, 429, 1, 14, 90, 350, 910, 1638, 2002

Offset: 0

Author

N. J. A. Sloane, Nov 09 2006

Keywords

• nonn
• easy
• tabf

Examples

			.......|...1
.......|.......1
.......|...1.......1
.......|.......2.......1
.......|...2.......3.......1
.......|.......5.......4.......1
.......|...5.......9.......5.......1
.......|......14......14.......6.......1
.......|..14......28......20.......7.......1
.......|......42......48......27.......8.......1
		

References

• J. H. Conway and D. A. Smith, On Quaternions and Octonions, A K Peters, Ltd., Natick, MA, 2003. See p. 60. MR1957212 (2004a:17002)

Links

• R. K. Guy, Catwalks, sandsteps and Pascal pyramids, J. Integer Sequences, Vol. 3 (2000), Article #00.1.6
• W. F. Klostermeyer, M. E. Mays, L. Soltes and G. Trapp, A Pascal rhombus, Fibonacci Quarterly, 35 (1997), 318-328.

Crossrefs

See A008315 (the main entry for this triangle) for more information.

Cf. A053121, A008313, A052173.

Programs

Maple

A008315 := proc(n,k)
    binomial(n,k)-binomial(n,k-1) ;
end:
for n from 0 to 30 do
    for k from 0 to n/2 do
        printf("%d, ",A008315(n,k)) ;
    od:
od: # R. J. Mathar, Feb 13 2008