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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A236453 Number of length n strings on the alphabet {0,1,2} of the form 0^i 1^j 2^k such that i,j,k>=0 and if i=1 then j=k. 1
 1, 3, 4, 8, 11, 17, 22, 30, 37, 47, 56, 68, 79, 93, 106, 122, 137, 155, 172, 192, 211, 233, 254, 278, 301, 327, 352, 380, 407, 437, 466, 498, 529, 563, 596, 632, 667, 705, 742, 782, 821, 863, 904, 948, 991, 1037, 1082, 1130, 1177, 1227, 1276, 1328, 1379, 1433, 1486, 1542 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The language of all such strings is an example of a language that satisfies the conditions of the pumping lemma for regular languages but is not regular. REFERENCES Michael Sipser, Introduction to the Theory of Computation, PWS Publishing Co., 1997, page 89. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..1000 FORMULA G.f.: (1 + x - 2*x^2 + 2*x^3)/((1 - x)^3*(1 + x)). For even n a(n) = A000124(n). For odd n a(n) = A000124(n) + 1. a(n) = (n^2 + n + 3 - (-1)^n)/2. - Giovanni Resta, Jan 26 2014 EXAMPLE a(3)=8 because we have: 000, 001, 002, 012, 111, 112, 122, 222. MATHEMATICA nn=40; a=1/(1-x); CoefficientList[Series[(a-x)a^2+x/(1-x^2), {x, 0, nn}], x] Table[(3 - (-1)^n + n + n^2)/2, {n, 0, 50}] (* Giovanni Resta, Jan 26 2014 *) PROG (PARI) a(n) = (n^2 + n + 3 - (-1)^n)/2 \\ Charles R Greathouse IV, Apr 18 2020 CROSSREFS Cf. A000124. Sequence in context: A133363 A186423 A156056 * A099108 A208971 A001994 Adjacent sequences: A236450 A236451 A236452 * A236454 A236455 A236456 KEYWORD nonn,easy AUTHOR Geoffrey Critzer, Jan 26 2014 EXTENSIONS Terms a(41) and beyond from Andrew Howroyd, Mar 27 2020 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 March 21 10:30 EDT 2023. Contains 361402 sequences. (Running on oeis4.)