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A108786 Yet another version of the Catalan triangle A008315. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A293600

Adjacent sequences:  A108783 A108784 A108785 * A108787 A108788 A108789

KEYWORD

nonn,easy,tabf

AUTHOR

N. J. A. Sloane, Nov 09 2006

STATUS

approved

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Last modified May 26 08:10 EDT 2018. Contains 304593 sequences. (Running on oeis4.)