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A136376
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a(n) = n*F(n) + (n-1)*F(n-1).
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2
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1, 3, 8, 18, 37, 73, 139, 259, 474, 856, 1529, 2707, 4757, 8307, 14428, 24942, 42941, 73661, 125951, 214739, 365166, 619508, 1048753, 1771943, 2988457, 5031843, 8459504, 14201994, 23811349, 39873841, 66695539, 111440227, 186016962
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| For n>2, mod 2 = (0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1,...), i.e. two evens followed by four odds, (repeating).
(1, 3, 8, 18, 37,...) = inverse binomial transform of A117202: (1, 4, 15, 52,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 03 2008]
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FORMULA
| a(n) = n*F(n) + (n-1)*F(n-1). Equals the matrix product A128064 (unsigned) * A000045.
a(n)=A045925(n)+A045925(n-1). a(n)=2*a(n-1)+a(n-2)-2*a(n-3)-a(n-4). G.f.: x*(1+x)*(1+x^2)/(x^2+x-1)^2. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 13 2009]
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EXAMPLE
| a(5) = 37 = a(n)*F(n) + (n-1)*F(n-1) = 5*5 + 4*3 = 25 + 12.
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MATHEMATICA
| Table[n*Fibonacci[n] + (n - 1)*Fibonacci[n - 1], {n, 1, 50}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Dec 28 2007
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CROSSREFS
| Cf. A000045, A128064.
A117202 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 03 2008]
Sequence in context: A004035 A169763 A000234 * A099845 A036635 A000713
Adjacent sequences: A136373 A136374 A136375 * A136377 A136378 A136379
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 28 2007
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EXTENSIONS
| More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Dec 28 2007
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