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A000667
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Boustrophedon transform of all-1's sequence.
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27
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1, 2, 4, 9, 24, 77, 294, 1309, 6664, 38177, 243034, 1701909, 13001604, 107601977, 959021574, 9157981309, 93282431344, 1009552482977, 11568619292914, 139931423833509, 1781662223749884, 23819069385695177
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Fill in a triangle, like Pascal's triangle, beginning each row with a 1 and filling in rows alternately right to left and left to right. Thus:
...............1.............
............1..->..2..........
.........4..<-.3...<-..1......
......1..->.5..->..8...->..9..
..............................
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
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).
N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).
N. J. A. Sloane, Transforms
Index entries for sequences related to boustrophedon transform
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FORMULA
| E.g.f.: exp(x) (tan x + sec x).
Lim n->infinity 2*n*a(n-1)/a(n) = Pi; lim n->infinity a(n)*a(n-2)/a(n-1)^2 = 1 + 1/(n-1) - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Aug 13 2004
a(n) = Sum_{k, k>=0} binomial(n, k)*A000111(n-k) . a(2n) = A000795(n) + A009747(n), a(2n+1) = A002084(n) + A003719(n) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 28 2005
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MATHEMATICA
| With[{nn=30}, CoefficientList[Series[Exp[x](Tan[x]+Sec[x]), {x, 0, nn}], x]Range[0, nn]!] (* From Harvey P. Dale, Nov 28 2011 *)
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CROSSREFS
| Absolute value of pairwise sums of A009337.
Sequence in context: A005001 A091151 A093542 * A131351 A091352 A135934
Adjacent sequences: A000664 A000665 A000666 * A000668 A000669 A000670
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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