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1, 2, 4, 6, 9, 13, 19, 28, 42, 64, 99, 155, 245, 390, 624, 1002, 1613, 2601, 4199, 6784, 10966, 17732, 28679, 46391, 75049, 121418, 196444, 317838, 514257, 832069, 1346299, 2178340, 3524610, 5702920, 9227499, 14930387, 24157853, 39088206
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) = F(n+1)-th highest positive integer not equal to any a(k), 1 <= k <= n-1, where F(n) = Fibonacci numbers = A000045(n). a(0) = 1, a(n) = a(n-1) + F(n+1) - F(n) + 1 = a(n-1) + A000045(n+1) - A000045(n) + 1 for n >= 1. a(0) = 1, a(n) = a(n-1) + F(n-1) + 1 = a(n-1) + A000045(n-1) + 1 for n >= 1. a(0) = 1, a(1) = 2, a(2) = 4, a(n) = a(n-1) + a(n-2) - (n-3) n >= 3. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Oct 28 2009]
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FORMULA
| a(n)=(sqrt(5)(1+sqrt(5))^(n+1)-sqrt(5)(1-sqrt(5))^(n+1))/(10*2^n)+n G.f.: (x^3+x-1)/((x-1)^2(x^2+x-1))
Row sums of triangle A135222 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 23 2007
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MAPLE
| (Mupad) numlib::fibonacci(n)+n-1 $ n = 1..48; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 08 2008
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MATHEMATICA
| Table[ Fibonacci[n+1]+n, {n, 0, 38}] (*From Vladimir Joseph Stephan Orlovsky, Apr 03 2011*)
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CROSSREFS
| Cf. A000045, A002062.
Cf. A135222.
Sequence in context: A171861 A039900 A039902 * A143586 A081225 A164140
Adjacent sequences: A081656 A081657 A081658 * A081660 A081661 A081662
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 26 2003
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