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!)
 A158799 a(0)=1, a(1)=2, a(n)=3 for n>=2. 17
 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) = number of neighboring natural numbers of n (i.e., n, n - 1, n + 1). a(n) = number of natural numbers m such that n - 1 <= m <= n + 1. Generalization: If a(n,k) = number of natural numbers m such that n - k <= m <= n + k (k >= 1) then a(n,k) = a(n-1,k) + 1 = n + k for 0 <= n <= k, a(n,k) = a(n-1,k) = 2k + 1 for n >= k + 1 (see, e.g., A158799). - Jaroslav Krizek, Nov 18 2009 Partial sums of A130716; partial sums give A008486. - Jaroslav Krizek, Dec 06 2009 In atomic spectroscopy, a(n) is the number of P term symbols with spin multiplicity equal to n+1, i.e., there is one singlet-P term (n=0), there are two doublet-P terms (n=1), and there are three P terms for triple multiplicity (n=2) and higher (n>2). - A. Timothy Royappa, Mar 16 2012 a(n+1) is also the domination number of the n-Andrasfai graph. - Eric W. Weisstein, Apr 09 2016 LINKS David Applegate, The movie version Eric Weisstein's World of Mathematics, Andrasfai Graph Eric Weisstein's World of Mathematics, Domination Number FORMULA G.f.: (1+x+x^2)/(1-x) = (1-x^3)/(1-x)^2. a(n) = (n>=0)+(n>=1)+(n>=2). a(n) = 3-2*[C(2*n,n) mod 2]-{C[(n+1)^2,n+3] mod 2}, with n>=0. - Paolo P. Lava, Mar 31 2009 a(n) = 1 + n for 0 <= n <= 1, a(n) = 3 for n >= 2. a(n) = A157532(n) for n >= 1. - Jaroslav Krizek, Nov 18 2009 E.g.f.: 3*exp(x) - x - 2= x^2/(2*G(0)) where G(k)= 1 + (k+2)/(x - x*(k+1)/(x + k + 1 - x^4/(x^3 +(k+1)*(k+2)*(k+3)/G(k+1)))); (continued fraction). - Sergei N. Gladkovskii, Jul 06 2012 a(n) = min(n+1,3). - Wesley Ivan Hurt, Apr 16 2014 MATHEMATICA PadRight[{1, 2}, 120, {3}] (* or *) Min[#, 3]&/@Range (* Harvey P. Dale, Apr 08 2018 *) PROG (PARI) a(n)=if(n>1, 3, if(n<0, 0, n++)) CROSSREFS Cf. A040000, A122553, A158411, A158478, A158515. Sequence in context: A192454 A270533 A244919 * A157532 A065684 A065683 Adjacent sequences:  A158796 A158797 A158798 * A158800 A158801 A158802 KEYWORD nonn,easy AUTHOR Jaume Oliver Lafont, Mar 27 2009 EXTENSIONS Corrected by Jaroslav Krizek, Dec 17 2009 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 July 10 12:53 EDT 2020. Contains 335576 sequences. (Running on oeis4.)