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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 triplet 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

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)/(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

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

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Last modified August 21 02:25 EDT 2017. Contains 290855 sequences.