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 A151798 a(0)=1, a(1)=2, a(n)=4 for n>=2. 6
 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 Index entries for linear recurrences with constant coefficients, signature (1). 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 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: A345438 A203638 A040002 * A334897 A035684 A049111 Adjacent sequences: A151795 A151796 A151797 * A151799 A151800 A151801 KEYWORD nonn,walk,easy AUTHOR David Applegate, Jun 29 2009 STATUS approved

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Last modified September 8 19:48 EDT 2024. Contains 375759 sequences. (Running on oeis4.)