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A132753
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a(n) = 2^(n+1) - n + 1.
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4
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3, 4, 7, 14, 29, 60, 123, 250, 505, 1016, 2039, 4086, 8181, 16372, 32755, 65522, 131057, 262128, 524271, 1048558, 2097133, 4194284, 8388587, 16777194, 33554409, 67108840, 134217703, 268435430, 536870885, 1073741796, 2147483619
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OFFSET
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0,1
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COMMENTS
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Apart from a(0): Row sums of triangle A132752 (old name).
Apart from a(0): Binomial transform of [1, 3, 0, 4, 0, 4, 0, 4, ...].
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LINKS
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FORMULA
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a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).
G.f.: (3 - 8*x + 6*x^2)/((1-x)^2 * (1-2*x)). (End)
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EXAMPLE
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a(3) = 14 = sum of row 3 terms of triangle A132752: (3 + 5 + 5 + 1).
a(3) = 14 = (1, 3, 3, 1) dot (1, 3, 0, 4) = (1 + 9 + 0 + 4).
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MAPLE
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MATHEMATICA
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PROG
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(PARI) a(n)=2^(n+1)-n+1
(PARI) Vec( (3-8*x+6*x^2)/((1-x)^2*(1-2*x)) + O(x^40)) \\ Colin Barker, Mar 14 2014
(Sage) [2^(n+1) -n+1 for n in (0..40)] # G. C. Greubel, Feb 16 2021
(Magma) [2^(n+1) -n+1: n in [0..40]]; // G. C. Greubel, Feb 16 2021
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CROSSREFS
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Cf. A003462, A007051, A024023, A029858, A034472, A052548, A058481, A067771, A079004, A100774, A115099, A134931. - Vladimir Joseph Stephan Orlovsky, Dec 25 2008
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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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Changed first member, and better name from Ralf Stephan, Aug 31 2013
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STATUS
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approved
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