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

Author

Jaume Oliver Lafont, Mar 27 2009

Keywords

• nonn
• easy

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

a(n+1) is also the domination number of the n X n rook complement graph. - Eric W. Weisstein, Mar 10 2025

Links

• David Applegate, The movie version
• Eric Weisstein's World of Mathematics, Andrásfai Graph.
• Eric Weisstein's World of Mathematics, Domination Number.
• Eric Weisstein's World of Mathematics, Rook Complement Graph.
• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

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

Cf. A008486, A130716.

Programs

Mathematica

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

PARI

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

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

Extensions

Corrected by Jaroslav Krizek, Dec 17 2009