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Search: id:A008280
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| A008280 |
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Boustrophedon version of triangle of Euler-Bernoulli or Entringer numbers read by rows. |
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+0
8
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| 1, 0, 1, 1, 1, 0, 0, 1, 2, 2, 5, 5, 4, 2, 0, 0, 5, 10, 14, 16, 16, 61, 61, 56, 46, 32, 16, 0, 0, 61, 122, 178, 224, 256, 272, 272, 1385, 1385, 1324, 1202, 1024, 800, 544, 272, 0, 0, 1385, 2770, 4094, 5296, 6320, 7120, 7664
(list; table; graph; listen)
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OFFSET
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0,9
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COMMENT
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The earliest known reference for this triangle is Seidel (1877). - D. E. Knuth, Jul 13 2007
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REFERENCES
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Arnold, V. I., Bernoulli-Euler updown numbers associated with function singularities, their combinatorics and arithmetics, Duke Math. J. 63 (1991), 537-555.
V. I. Arnold, The calculus of snakes and the combinatorics of Bernoulli, Euler and Springer numbers of Coxeter groups, Uspekhi Mat. nauk., 47 (#1, 1992), 3-45 = Russian Math. Surveys, Vol. 47 (1992), 1-51.
M. D. Atkinson: Zigzag permutations and comparisons of adjacent elements, Information Processing Letters 21 (1985), 187-189.
M. D. Atkinson: Partial orders and comparison problems, Sixteenth Southeastern Conference on Combinatorics, Graph Theory and Computing, (Boca Raton, Feb 1985), Congressus Numerantium 47, 77-88.
J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 110.
A. J. Kempner, On the shape of polynomial curves, Tohoku Math. J., 37 (1933), 347-362.
C. Poupard, De nouvelles significations enumeratives des nombres d'Entringer, Discrete Math., 38 (1982), 265-271.
L. Seidel, Ueber eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen, Sitzungsberichte der mathematisch-physikalischen Classe der k\"oniglich bayerischen Akademie der Wissenschaften zu M\"unchen, volume 7 (1877), 157-187.
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LINKS
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B. Gourevitch, L'univers de Pi
J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon on transform, J. Combin. Theory, 17A 44-54 1996 (Abstract, pdf, ps).
R. Street, Trees, permutations and the tangent function
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EXAMPLE
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This version of the triangle begins:
.............1
...........0...1
.........1...1...0
.......0...1...2...2
.....5...5...4...2...0
...0...5..10..14..16..16
See A008281 and A108040 for other versions.
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CROSSREFS
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Cf. A008281.
Sequence in context: A045537 A161622 A116559 this_sequence A063960 A025510 A158106
Adjacent sequences: A008277 A008278 A008279 this_sequence A008281 A008282 A008283
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KEYWORD
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nonn,tabl,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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