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A072176
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Unimodal analogue of Fibonacci numbers: a(n+1)=sum_k A071922(n-k,k).
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3
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1, 1, 2, 3, 5, 9, 16, 30, 56, 106, 201, 382, 727, 1384, 2636, 5021, 9565, 18222, 34715, 66137, 126001, 240052, 457338, 871304, 1659978, 3162533, 6025150, 11478911, 21869232, 41664520, 79377833, 151227961, 288114394, 548905795
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Based on the observation that F_{n+1}=sum_k binomial (n-k,k). In both cases the sum is extended to 0<=2k<=n.
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FORMULA
| G.f.: x(-x^2-x+1)/[(1-x)(1-x-2x^2+x^4)].
a(0)=0, a(1)=1, a(2)=1, a(3)=2, a(4)=3, a(n)=2*a(n-1)+a(n-2)-2*a(n-3)- a(n-4)+a(n-5) [From Harvey P. Dale, June 23 2011]
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MATHEMATICA
| Rest[LinearRecurrence[{2, 1, -2, -1, 1}, {0, 1, 1, 2, 3}, 40]] (* or *) CoefficientList[ Series[x (-x^2-x+1)/((1-x)(1-x-2x^2+x^4)), {x, 0, 40}], x] (* From Harvey P. Dale, June 23 2011 *)
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CROSSREFS
| Cf. A071922, A005578.
Sequence in context: A198518 A107250 A050168 * A047061 A136169 A047041
Adjacent sequences: A072173 A072174 A072175 * A072177 A072178 A072179
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KEYWORD
| nonn,easy
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AUTHOR
| Michele Dondi (bik.mido(AT)tiscalinet.it), Jun 30, 2002
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