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Search: id:A099919
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| A099919 |
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F(3) + F(6) + F(9) +...+ F(3n), F(n) = Fibonacci numbers A000045. |
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+0
4
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| 2, 10, 44, 188, 798, 3382, 14328, 60696, 257114, 1089154, 4613732, 19544084, 82790070, 350704366, 1485607536, 6293134512, 26658145586, 112925716858, 478361013020, 2026369768940, 8583840088782, 36361730124070
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OFFSET
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1,1
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REFERENCES
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A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 25.
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FORMULA
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(1/2) (Fibonacci(3n+2) - 1). G.f.: 2/[(1-x)(1-4x-x^2)].
a(n)=sum_{0<=j<=i<=n} binomial(i, j)*F(i+j) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 21 2005
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CROSSREFS
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Equals 2 * A049652(n).
Partial sums of A014445. Equals (1/2)(A015448(n+1)-1). Cf. A004794.
Cf. A087635.
Sequence in context: A122932 A080069 A068551 this_sequence A100397 A084059 A084609
Adjacent sequences: A099916 A099917 A099918 this_sequence A099920 A099921 A099922
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan, Oct 30 2004
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