cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A090326 Number of rules of a context-free grammar in Chomsky normal form that generates all permutations of n symbols.

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%I A090326 #22 Apr 26 2023 08:54:58
%S A090326 1,4,15,54,185,608,1939,6058,18669,57012,173063,523262,1577953,
%T A090326 4750216,14283387,42915666,128878037,386896220,1161212911,3484687270,
%U A090326 10456158921,31372671024,94126401635,282395982074,847221500605,2541731610628,7625329049559
%N A090326 Number of rules of a context-free grammar in Chomsky normal form that generates all permutations of n symbols.
%H A090326 Colin Barker, <a href="/A090326/b090326.txt">Table of n, a(n) for n = 1..1000</a>
%H A090326 P. R. J. Asveld, <a href="http://dx.doi.org/10.1016/j.tcs.2005.11.010">Generating all permutations by context-free grammars in Chomsky normal form</a>, Theoretical Computer Science 354 (2006) 118-130.
%H A090326 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-17,17,-6).
%F A090326 a(n) = 3^n - 2^(n+1) + n + 1.
%F A090326 G.f.: x*(4*x^2-3*x+1) / ((x-1)^2*(2*x-1)*(3*x-1)). - _Colin Barker_, Jan 15 2015
%F A090326 E.g.f.: exp(x)*(1 - 2*exp(x) + exp(2*x) + x). - _Stefano Spezia_, Apr 25 2023
%e A090326 S -> AD | DA | BE | EB | CF | FC, D -> BC | CB, E -> AC | CA, F -> AB | BA, A -> a, B -> b, C -> c; so a(3)=15.
%t A090326 f[n_] := 3^n - 2^(n + 1) + n + 1; Table[ f[n], {n, 1, 26}] (* _Robert G. Wilson v_, Jan 30 2004 *)
%o A090326 (PARI) Vec(x*(4*x^2-3*x+1)/((x-1)^2*(2*x-1)*(3*x-1)) + O(x^100)) \\ _Colin Barker_, Jan 15 2015
%K A090326 nonn,easy
%O A090326 1,2
%A A090326 _Peter R. J. Asveld_, Jan 27 2004
%E A090326 More terms from _Robert G. Wilson v_, Jan 30 2004