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A108786
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Yet another version of the Catalan triangle A008315.
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1
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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)
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OFFSET
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0,6
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REFERENCES
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J. H. Conway and D. A. Smith, On Quaternions and Octonions, A K Peters, Ltd., Natick, MA, 2003. See p. 60. MR1957212 (2004a:17002)
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LINKS
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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.
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EXAMPLE
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.......|...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
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MAPLE
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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
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CROSSREFS
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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
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KEYWORD
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nonn,easy,tabf
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AUTHOR
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N. J. A. Sloane, Nov 09 2006
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STATUS
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approved
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