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Search: id:A129973
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| 0, 0, 0, 1, 1, 3, 5, 9, 16, 27, 46, 77, 128, 212, 349, 573, 938, 1532, 2498, 4067, 6614, 10746, 17446, 28306, 45903, 74409, 120577, 195337, 316379, 512332, 829527, 1342940, 2173899, 3518736, 5695148, 9217213, 14916771, 24139826, 39064336
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OFFSET
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1,6
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COMMENT
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Difference between the Fibonacci sequence A000045 and the Padovan sequence A000931. Always >= 0.
Limit Table[N[(Fibonacci[n + 1] - a[n + 1])/(Fibonacci[n] - a[n])], {n, 4, 40}]; limit[a(n+1)/a(n),n->Infinity]->(1+Sqrt[5])/2
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FORMULA
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G.f.: x^4/((1-x-x^2)(1-x^2-x^3)). a(n)=a(n-1)+2*a(n-2)-2*a(n-4)-a(n-5). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 30 2008]
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MATHEMATICA
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(* Minimal Pisot sequence sequence : A000931 : Padovan sequence*) a[0] = 0; a[1] = 1; a[2] = 1; a[n_] := a[n] = a[n - 2] + a[n - 3]; aa = Table[Fibonacci[n] - a[n], {n, 0, 40}]
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CROSSREFS
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Cf. A000045, A000931.
Sequence in context: A117480 A018260 A023656 this_sequence A018159 A094980 A069818
Adjacent sequences: A129970 A129971 A129972 this_sequence A129974 A129975 A129976
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 13 2007
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