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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; internal format)
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OFFSET
| 0,6
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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)
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LINKS
| R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, J. Integer Seqs., Vol. 3 (2000), #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
| .......|...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
| 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 (mathar(AT)strw.leidenuniv.nl), Feb 13 2008
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CROSSREFS
| See A008315 (the main entry for this triangle) for more information.
Cf. A053121, A008313, A052173.
Sequence in context: A181847 A165999 A049280 * A008315 A191318 A191395
Adjacent sequences: A108783 A108784 A108785 * A108787 A108788 A108789
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KEYWORD
| nonn,easy,tabf
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 09 2006
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 13 2008
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