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A093960
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a(1) = 1, a(2) = 2, a(n + 1) = n*a(1) + (n-1)*a(2) + ...(n-r)*a(r + 1) + ... + a(n).
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1
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1, 2, 4, 11, 29, 76, 199, 521, 1364, 3571, 9349, 24476, 64079, 167761, 439204, 1149851, 3010349, 7881196, 20633239, 54018521, 141422324, 370248451, 969323029, 2537720636, 6643838879, 17393796001, 45537549124, 119218851371
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(1)=a(2) = 1 gives A088305 i.e. fibonacci numbers with even indices. This can be called 'fake Fibonacci sequence'. 4 = 3+1, 11 = 8+3, 29 = 21+8, 76 = 55+21, etc. a(n) = F(2n-2) + F(2n-4).
Except for the initial terms, this is the same as the bisection of the Lucas sequence (A002878). - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jul 17 2006
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FORMULA
| a(n) = F(2n-2) + F(2n-4), where F(k) is k-th Fibonacci number, n >2.
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MAPLE
| a[1]:=1: a[2]:=2: for n from 2 to 33 do a[n+1]:=sum((n-r)*a[r+1], r=0..n-1) od: seq(a[n], n=1..33); (Deutsch)
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MATHEMATICA
| Print[1]; Print[2]; Do[Print[Fibonacci[2*n - 2] + Fibonacci[2*n - 4]], {n, 3, 20}] (Propper)
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CROSSREFS
| Cf. A088305.
Sequence in context: A005503 A148139 A061860 * A118311 A132836 A148140
Adjacent sequences: A093957 A093958 A093959 * A093961 A093962 A093963
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), May 22 2004
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EXTENSIONS
| More terms from Ryan Propper (rpropper(AT)stanford.edu), Jun 19 2005
More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 01 2005
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