The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A000667 Boustrophedon transform of all-1's sequence. 37
 1, 2, 4, 9, 24, 77, 294, 1309, 6664, 38177, 243034, 1701909, 13001604, 107601977, 959021574, 9157981309, 93282431344, 1009552482977, 11568619292914, 139931423833509, 1781662223749884, 23819069385695177, 333601191667149054, 4884673638115922509 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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. Row sums of triangle A109449. - Reinhard Zumkeller, Nov 04 2013 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..485 (first 101 terms from T. D. Noe) C. K. Cook, M. R. Bacon, and R. A. Hillman, Higher-order Boustrophedon transforms for certain well-known sequences, Fib. Q., 55(3) (2017), 201-208. Peter Luschny, An old operation on sequences: the Seidel transform. J. Millar, N. J. A. Sloane, and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory Ser. A, 76(1) (1996), 44-54 (Abstract, pdf, ps). J. Millar, N. J. A. Sloane, and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory Ser. A, 76(1) (1996), 44-54. Ludwig Seidel, Über eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, volume 7 (1877), 157-187. [USA access only through the HATHI TRUST Digital Library] Ludwig Seidel, Über eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, volume 7 (1877), 157-187. [Access through ZOBODAT] N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98). N. J. A. Sloane, Transforms. Wikipedia, Boustrophedon transform. FORMULA E.g.f.: exp(x) * (tan(x) + sec(x)). Limit_{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, Aug 13 2004 a(n) = Sum_{k=0..n} binomial(n, k)*A000111(n-k). a(2*n) = A000795(n) + A009747(n), a(2*n+1) = A002084(n) + A003719(n). - Philippe Deléham, Aug 28 2005 a(n) = A227862(n, n * (n mod 2)). - Reinhard Zumkeller, Nov 01 2013 G.f.: E(0)*x/(1-x)/(1-2*x) + 1/(1-x), where E(k) = 1 - x^2*(k + 1)*(k + 2)/(x^2*(k + 1)*(k + 2) - 2*(x*(k + 2) - 1)*(x*(k + 3) - 1)/E(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Jan 16 2014 a(n) ~ n! * exp(Pi/2) * 2^(n+2) / Pi^(n+1). - Vaclav Kotesovec, Jun 12 2015 EXAMPLE ...............1.............. ............1..->..2.......... .........4..<-.3...<-..1...... ......1..->.5..->..8...->..9.. MATHEMATICA With[{nn=30}, CoefficientList[Series[Exp[x](Tan[x]+Sec[x]), {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Nov 28 2011 *) t[_, 0] = 1; t[n_, k_] := t[n, k] = t[n, k-1] + t[n-1, n-k]; a[n_] := t[n, n]; Array[a, 30, 0] (* Jean-François Alcover, Feb 12 2016 *) PROG (Sage) # Algorithm of L. Seidel (1877) def A000667_list(n) : R = []; A = {-1:0, 0:0} k = 0; e = 1 for i in range(n) : Am = 1 A[k + e] = 0 e = -e for j in (0..i) : Am += A[k] A[k] = Am k += e # print [A[z] for z in (-i//2..i//2)] R.append(A[e*i//2]) return R A000667_list(10) # Peter Luschny, Jun 02 2012 (Haskell) a000667 n = if x == 1 then last xs else x where xs@(x:_) = a227862_row n -- Reinhard Zumkeller, Nov 01 2013 (PARI) x='x+O('x^33); Vec(serlaplace( exp(x)*(tan(x) + 1/cos(x)) ) ) \\ Joerg Arndt, Jul 30 2016 (Python) from itertools import islice, accumulate def A000667_gen(): # generator of terms blist = tuple() while True: yield (blist := tuple(accumulate(reversed(blist), initial=1)))[-1] A000667_list = list(islice(A000667_gen(), 20)) # Chai Wah Wu, Jun 11 2022 CROSSREFS Absolute value of pairwise sums of A009337. Column k=1 of A292975. Cf. A000111, A000795, A009747, A002084, A003719, A109449, A227862. Sequence in context: A091151 A093542 A301927 * A131351 A091352 A135934 Adjacent sequences: A000664 A000665 A000666 * A000668 A000669 A000670 KEYWORD nonn,easy,nice AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 5 08:51 EST 2022. Contains 358585 sequences. (Running on oeis4.)