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A084172
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a(n) = +3*a(n-1) -1*a(n-2) -3*a(n-3) +2*a(n-4).
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4
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1, 2, 4, 9, 19, 40, 82, 167, 337, 678, 1360, 2725, 5455, 10916, 21838, 43683, 87373, 174754, 349516, 699041, 1398091, 2796192, 5592394, 11184799, 22369609, 44739230, 89478472, 178956957, 357913927, 715827868, 1431655750, 2863311515
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Original name was: Generalized Jacobsthal numbers.
Sums of rows of the triangle in A109225. - Reinhard Zumkeller, Jun 23 2005
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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FORMULA
| a(n)=2^(n+2)/3-(-1)^n/12-(2*n+1)/4.
G.f: (2*x^3 - x^2 - x + 1)/(-2*x^4 + 3*x^3 + x^2 - 3*x + 1).
a(n+2)=a(n+1)+2*a(n)+n, a(0)=0, a(1)=2.
a(n) = A001045(n+1) + A083579(n).
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PROG
| (MAGMA) [2^(n+2)/3-(-1)^n/12-(2*n+1)/4: n in [0..35]]; // Vincenzo Librandi, Jul 05 2011
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CROSSREFS
| Sequence in context: A018001 A018099 A011955 * A018100 A052908 A036616
Adjacent sequences: A084169 A084170 A084171 * A084173 A084174 A084175
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 18 2003
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