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Search: id:A007574
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| A007574 |
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Patterns in a dual ring.
(Formerly M2653)
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+0
1
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| 1, 3, 7, 15, 31, 60, 113, 207, 373, 663, 1167, 2038, 3537, 6107, 10499, 17983, 30703, 52272, 88769, 150407, 254321, 429223, 723167, 1216490, 2043361, 3427635, 5742463, 9609327, 16062463, 26821668, 44744657
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
C. A. Church, Jr., Lattice paths and Fibonacci and Lucas numbers, Fibonacci Quarterly 12(4) (1974) 336-338.
W. Dotson, F. Norwood and C. Taylor, Fiber optics and Fibonacci, Math. Mag., 66 (1993), 167-174.
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MAPLE
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with(combinat): A007574 := proc(n) local k; if n=1 then RETURN(1) fi; if n=2 then RETURN(3) fi; if n=3 then RETURN(7) fi; if n>3 then RETURN( fibonacci(n)+2*fibonacci(n-1)+n*sum(fibonacci(n-k), k=2..n-1)) fi; end;
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MATHEMATICA
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Table[ Fibonacci[n] + 2 Fibonacci[n - 1] + n*Sum[Fibonacci[n - k], {k, 2, n - 1}], {n, 1, 35} ]
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CROSSREFS
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Cf. A000045.
Sequence in context: A151338 A023424 A006778 this_sequence A034480 A057703 A006739
Adjacent sequences: A007571 A007572 A007573 this_sequence A007575 A007576 A007577
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KEYWORD
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nonn
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AUTHOR
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Simon Plouffe, N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
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