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A060013
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New record highs reached in A060000.
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6
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1, 2, 3, 5, 9, 15, 27, 51, 99, 195, 387, 771, 1539, 3075, 6147, 12291, 24579, 49155, 98307, 196611, 393219, 786435, 1572867, 3145731, 6291459, 12582915, 25165827, 50331651, 100663299, 201326595, 402653187, 805306371, 1610612739
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OFFSET
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1,2
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LINKS
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FORMULA
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For n>4: a(n) =2a(n-1)-3. For n>3: a(n) =3*2^(n-3)+3 =3*A000051(n-3) =A007283(n-3)+3.
G.f.: -x*(x^2-x+1)*(2*x^3+2*x^2-1) / ((x-1)*(2*x-1)). - Colin Barker, Jan 12 2013
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MATHEMATICA
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h = f = {1, 2}; a = 1; b = 2; Do[ g = Sort[ h ]; If[ g[ [ -1 ] ] + 1 == n, c = a + b, k = 1; While[ g[ [ k ] ] == k, k++ ]; c = k ]; a = b; b = c; h = Append[ h, c ]; If[ c > g[ [ -1 ] ], f = Append[ f, c ] ], { n, 3, 10^4 } ]; f
LinearRecurrence[{3, -2}, {1, 2, 3, 5, 9, 15}, 40] (* Harvey P. Dale, Dec 12 2018 *)
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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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EXTENSIONS
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Formulae and more terms from Henry Bottomley and Larry Reeves (larryr(AT)acm.org), Mar 19 2001
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STATUS
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approved
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