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A081662
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Partial sums of n+F(n+1).
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2
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1, 3, 7, 13, 22, 35, 54, 82, 124, 188, 287, 442, 687, 1077, 1701, 2703, 4316, 6917, 11116, 17900, 28866, 46598, 75277, 121668, 196717, 318135, 514579, 832417, 1346674, 2178743, 3525042, 5703382, 9227992, 14930912, 24158411, 39088798
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| Harvey P. Dale, Table of n, a(n) for n = 0..1000
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FORMULA
| a(n)=(1-2sqrt(5)/5)(sqrt(5)/2-1/2)^n(-1)^n+(sqrt(5)/2+1/2)^n(2sqrt(5)/5+1)+(n^2+n-2)/2 G.f.: (x^3+x-1)/((1-x)^3(x^2+x-1))
Row sums of triangle A132923, = binomial transform of (1, 2, 2, 0, 1, -1, 2, -3, 5, -8,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 05 2007
a(0)=1, a(1)=3, a(2)=7, a(3)=13, a(4)=22, a(n)=4*a(n-1)-5*a(n-2)+a(n-3)+2*a(n-4)-a(n-5) [From Harvey P. Dale, Nov 19 2011]
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MATHEMATICA
| Accumulate[Table[Total[{n, Fibonacci[n+1]}], {n, 0, 40}]] (* or *) LinearRecurrence[ {4, -5, 1, 2, -1}, {1, 3, 7, 13, 22}, 41] (* From Harvey P. Dale, Nov 19 2011 *)
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CROSSREFS
| Cf. A081659, A000045.
Cf. A132923.
Sequence in context: A051336 A002623 A173196 * A091652 A134197 A053001
Adjacent sequences: A081659 A081660 A081661 * A081663 A081664 A081665
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 26 2003
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