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A151798 a(0)=1, a(1)=2, a(n)=4 for n>=2. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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

Table of n, a(n) for n=0..101.

David Applegate, The movie version

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

MATHEMATICA

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

PROG

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

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

CROSSREFS

Cf. A010709, A131098, A077996, A105696.

Sequence in context: A105192 A203638 A040002 * A334897 A035684 A049111

Adjacent sequences:  A151795 A151796 A151797 * A151799 A151800 A151801

KEYWORD

nonn,walk

AUTHOR

David Applegate, Jun 29 2009

STATUS

approved

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Last modified March 3 10:45 EST 2021. Contains 341762 sequences. (Running on oeis4.)