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A083706
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a(n) = 2^(n+1)+n-1.
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15
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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
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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FORMULA
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G.f.: (1-2*x^2)/((1-x)^2*(1-2*x)).
a(n) = 2*a(n-1) + 3 - n.
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MATHEMATICA
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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 *)
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PROG
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(PARI) a(n)=if(n<0, 0, 2^(n+1)+n-1)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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