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A151798
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a(0)=1, a(1)=2, a(n)=4 for n>=2.
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4
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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
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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Table of n, a(n) for n=0..101.
David Applegate, The movie version
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FORMULA
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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
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MATHEMATICA
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f[n_] := Fold[#2*Floor[#1/#2 + 1/2] &, n, Reverse@ Range[n - 1]]; Array[f, 55]
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PROG
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(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
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CROSSREFS
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Cf. A010709, A131098, A077996, A105696.
Sequence in context: A105192 A203638 A040002 * A334897 A035684 A049111
Adjacent sequences: A151795 A151796 A151797 * A151799 A151800 A151801
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KEYWORD
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nonn,walk
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AUTHOR
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David Applegate, Jun 29 2009
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STATUS
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approved
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