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A070550
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a(n) = a(n-1) + a(n-3) + a(n-4), starting with a(0..3) = 1, 2, 2, 3.
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9
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1, 2, 2, 3, 6, 10, 15, 24, 40, 65, 104, 168, 273, 442, 714, 1155, 1870, 3026, 4895, 7920, 12816, 20737, 33552, 54288, 87841, 142130, 229970, 372099, 602070, 974170, 1576239, 2550408, 4126648, 6677057, 10803704, 17480760, 28284465, 45765226
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Shares some properties with Fibonacci sequence.
The sum of any two alternating terms (terms separated by one other term) produces a Fibonacci number (e.g. 2+6=8, 3+10=13, 24+65=89, etc.) The product of any two consecutive or alternating Fibonacci terms produces a term from this series. (e.g. 5x8=40, 13x5=65, 21x8=168, etc.)
In Penney's game (see A171861), ways that HTH beats HHH on flip 3,4,5,... [Ed Pegg Jr, Dec 02 2010]
The Ca2 sums, see A180662 for the definition of these sums, of triangle A035607 equal the terms of this sequence. [Johannes W. Meijer, Aug 05 2011]
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
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FORMULA
| a(n) = F[floor(n/2)+1]*F[ceiling(n/2)+2], with F(n) = A000045(n). - R. Stephan, Apr 14 2004
G.f.: (1+x)/(1-x-x^3-x^4) = (1+x)/((1+x^2)*(1-x-x^2))
a(n) = a(n-1) + a(n-3) + a(n-4)
a(n) = A126116(n+4) - F(n+3) [Johannes W. Meijer, Aug 05 2011]
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MAPLE
| with(combinat): A070550 := proc(n): fibonacci(floor(n/2)+1)*fibonacci(ceil(n/2)+2) end: seq(A070550(n), n=0..37); [Johannes W. Meijer, Aug 05 2011]
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PROG
| (Haskell)
a070550 n = a070550_list !! n
a070550_list = 1 : 2 : 2 : 3 :
zipWith (+) a070550_list
(zipWith (+) (tail a070550_list) (drop 3 a070550_list))
-- Reinhard Zumkeller, Aug 06 2011
(PARI) A070550(n) = fibonacci(n\2+1)*fibonacci((n+5)\2) \\ - M. F. Hasler, Aug 6 2011
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CROSSREFS
| a(2*n) = F(n+1)*F(n+2) = A001654(n+1), a(2*n+1) = F(n+1)*F(n+3) = A059929(n+1).
Cf. A049853.
Sequence in context: A163493 A054200 A137216 * A145778 A102762 A049853
Adjacent sequences: A070547 A070548 A070549 * A070551 A070552 A070553
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KEYWORD
| easy,nonn
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AUTHOR
| Sreyas Srinivasan (sreyas_srinivasan(AT)hotmail.com), May 02 2002
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EXTENSIONS
| More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), May 03 2002
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