A151798 a(0)=1, a(1)=2, a(n)=4 for n>=2.

1, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset: 0

Author

David Applegate, Jun 29 2009

Keywords

• nonn
• walk
• easy

Comments

A010709 preceded by 1, 2.

Partial sums give A131098.

The INVERT transform gives A077996 without A077996(0). The Motzkin transform gives A105696 without A105696(0). Decimal expansion of 28/225=0.12444... . - R. J. Mathar, Jun 29 2009

Continued fraction expansion of 1 + sqrt(1/5). - Arkadiusz Wesolowski, Mar 30 2012

The number of solutions x (mod 2^(n+1)) of x^2 = 1 (mod 2^(n+1)), namely x = 1 (n=0), x = -1, 1 (n=1) and x = -1, 1, 2^n-1, 2^n+1 (n at least 2). - Christopher J. Smyth, May 15 2014

Also, the number of n-step self-avoiding walks on the L-lattice with no non-contiguous adjacencies (see A322419 for details of L-lattice). - Sean A. Irvine, Jul 29 2020

Links

• David Applegate, The movie version
• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A010709, A131098, A077996, A105696.

Programs

Magma

[ n le 1 select n+1 else 4: n in [0..104] ];

Mathematica

f[n_] := Fold[#2*Floor[#1/#2 + 1/2] &, n, Reverse@ Range[n - 1]]; Array[f, 55]

PARI

Vec((1+x+2*x^2)/(1-x) + O(x^100)) \\ Altug Alkan, Jan 19 2016

Formula

G.f.: (1+x+2*x^2)/(1-x).

E.g.f. A(x)=x*B(x) satisfies the differential equation B'(x)=1+x+x^2+B(x). - Vladimir Kruchinin, Jan 19 2011

E.g.f.: 4*exp(x) - 2*x - 3. - Elmo R. Oliveira, Aug 06 2024