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 A083706 a(n) = 2^(n+1)+n-1. 14
 1, 4, 9, 18, 35, 68, 133, 262, 519, 1032, 2057, 4106, 8203, 16396, 32781, 65550, 131087, 262160, 524305, 1048594, 2097171, 4194324, 8388629, 16777238, 33554455, 67108888, 134217753, 268435482, 536870939, 1073741852, 2147483677, 4294967326, 8589934623 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Warning: not all quizzes permit the use of the OEIS! Is A247983(n+1) = A247983(n) if and only if n is in A083706? - Clark Kimberling, Sep 28 2014 a(n) is the least number of nodes in a height-n 2-3-4 tree, if using the top-down insertion algorithm and there have been no deletions. - Daniel S. Roche, Oct 05 2014 Also the number of independent vertex sets and vertex covers in the n-crown graph. - Andrew Howroyd, May 14 2017 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 C. P. Simoes, Mental Performance Test, 2003. [Broken link] Eric Weisstein's World of Mathematics, Crown Graph Eric Weisstein's World of Mathematics, Independent Vertex Set Eric Weisstein's World of Mathematics, Vertex Cover FORMULA G.f.: (1-2*x^2)/((1-x)^2*(1-2*x)). a(n) = 2*a(n-1) + 3 - n. Row sums of A130301. - Gary W. Adamson, May 20 2007 MATHEMATICA Table[2^(n + 1) + n - 1, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 19 2011 *) LinearRecurrence[{4, -5, 2}, {4, 9, 18}, {0, 20}] (* Eric W. Weisstein, Sep 21 2017 *) CoefficientList[Series[(-1 + 2 x^2)/((-1 + x)^2 (-1 + 2 x)), {x, 0, 20}], x] (* Eric W. Weisstein, Sep 21 2017 *) PROG (PARI) a(n)=if(n<0, 0, 2^(n+1)+n-1) (MAGMA) [2^(n+1)+n-1: n in [0..35]]; // Vincenzo Librandi, Jul 20 2011 CROSSREFS Cf. A130301, A160692, A247983. Sequence in context: A320851 A027053 A122039 * A229072 A261983 A074896 Adjacent sequences:  A083703 A083704 A083705 * A083707 A083708 A083709 KEYWORD nonn AUTHOR N. J. A. Sloane, Jun 15 2003 STATUS approved

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Last modified January 19 14:53 EST 2020. Contains 331049 sequences. (Running on oeis4.)