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

0,6

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

Table of n, a(n) for n=0..70.

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.

Example

.......|...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

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

Crossrefs

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

Cf. A053121, A008313, A052173.

Sequence in context: A239030 A165999 A049280 * A008315 A191318 A341315

Adjacent sequences: A108783 A108784 A108785 * A108787 A108788 A108789

Keyword

nonn,easy,tabf

Author

N. J. A. Sloane, Nov 09 2006

Status

approved