

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
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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(n1,k) + 1 = n + k for 0 <= n <= k, a(n,k) = a(n1,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 singletP term (n=0), there are two doubletP terms (n=1), and there are three P terms for triplet multiplicity (n=2) and higher (n>2).  A. Timothy Royappa, Mar 16 2012
a(n+1) is also the domination number of the nAndrasfai graph.  Eric W. Weisstein, Apr 09 2016


LINKS

Table of n, a(n) for n=0..86.
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)/(1x) = (1x^3)/(1x)^2.
a(n) = (n>=0)+(n>=1)+(n>=2).
a(n) = 32*[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


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



