A158799 a(0)=1, a(1)=2, a(n)=3 for n >= 2.

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

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) = 2*k + 1 for n >= k + 1. - 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-Andrásfai graph. - Eric W. Weisstein, Apr 09 2016

Decimal expansion of 37/300. - Elmo R. Oliveira, May 11 2024

Links

Table of n, a(n) for n=0..86.

David Applegate, The movie version

Eric Weisstein's World of Mathematics, Andrásfai Graph

Eric Weisstein's World of Mathematics, Domination Number

Index entries for linear recurrences with constant coefficients, signature (1).

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) = 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

a(n) = 1 + A130130(n). - Elmo R. Oliveira, May 11 2024

Mathematica

PadRight[{1, 2}, 120, {3}] (* or *) Min[#, 3]&/@Range[120] (* Harvey P. Dale, Apr 08 2018 *)

Prog

(PARI) a(n)=if(n>1, 3, if(n<0, 0, n++))

Crossrefs

Cf. A040000, A122553, A130130, A139250, A157532, A158411, A158478, A158515.

Cf. A008486, A130716.

Sequence in context: A270533 A344511 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