The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A129952 Binomial transform of A124625. 9
 1, 1, 2, 6, 16, 40, 96, 224, 512, 1152, 2560, 5632, 12288, 26624, 57344, 122880, 262144, 557056, 1179648, 2490368, 5242880, 11010048, 23068672, 48234496, 100663296, 209715200, 436207616, 905969664, 1879048192, 3892314112 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Essentially the same as A057711: a(n) = A057711(n) for n >= 1. Number of permutations of length n>=0 avoiding the partially ordered pattern (POP) {1>2, 1>3} of length 4. That is, number of length n permutations having no subsequences of length 4 in which the first element is larger than the second and third elements. - Sergey Kitaev, Dec 08 2020 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Alice L. L. Gao, Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, arXiv:1903.08946 [math.CO], 2019. Alice L. L. Gao, Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, The Electronic Journal of Combinatorics 26(3) (2019), P3.26. Index entries for linear recurrences with constant coefficients, signature (4,-4). FORMULA a(0) = 1, a(1) = 1; for n > 1, a(n) = n*2^(n-2). G.f.: (1-3*x+2*x^2+2*x^3)/(1-2*x)^2. E.g.f.: (1/2)*(x*exp(2*x) + x + 2). - G. C. Greubel, Jun 08 2016 MATHEMATICA LinearRecurrence[{4, -4}, {1, 1, 2, 6}, 30] (* G. C. Greubel, Jun 08 2016; corrected by Georg Fischer, Apr 02 2019 *) PROG (MAGMA) m:=15; S:=&cat[ [ 1, 2*i ]: i in [0..m] ]; [ &+[ Binomial(j-1, k-1)*S[k]: k in [1..j] ]: j in [1..2*m] ]; // Klaus Brockhaus, Jun 17 2007 (PARI) {m=29; print1(1, ", ", 1, ", "); for(n=2, m, print1(n*2^(n-2), ", "))} \\ Klaus Brockhaus, Jun 17 2007 CROSSREFS Cf. A124625, A045623, A057711, A129953 (first differences), A129954 (second differences), A129955 (third differences). Sequence in context: A078774 A174016 A265725 * A057711 A302239 A264551 Adjacent sequences:  A129949 A129950 A129951 * A129953 A129954 A129955 KEYWORD nonn,easy AUTHOR Paul Curtz, Jun 10 2007 EXTENSIONS Edited and extended by Klaus Brockhaus, Jun 17 2007 STATUS approved

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

Last modified August 1 22:36 EDT 2021. Contains 346408 sequences. (Running on oeis4.)